No.  You are not required to use your Medicare Part D plan even when you are buying a formulary drug at one of your Medicare plan's network pharmacies.

However, except in certain situations (explained below), you may not be reimbursed for any drug purchases you make without using your Medicare Part D plan.

Cash Purchases without the Donut Hole Discount
Also, if you do not use your Medicare Part D plan when purchasing your medications at a network pharmacy, you will not be able to take advantage of the Donut Hole or Coverage Gap discount.  As noted by the Centers for Medicare and Medicaid Services (CMS):
 

"Part D sponsors shall provide the applicable [Donut Hole] discount for out-of-network paper claims submitted by Part D enrollees. However, the discount shall not apply to in-network claims that were not submitted electronically by the pharmacy for any reason other than the pharmacy was technically unable to process claims on the date of service through no fault of the beneficiary. This means that beneficiaries that choose to have a prescription filled for a “better cash price” that is not processed through the Part D sponsor will not receive a manufacturer discount under the Discount Program on such prescription." [emphasis added]

(Source: CMS Memo, April 30, 2011, Medicare Coverage Gap Discount Program beginning in 2011, Section 70.5 Point-of-sale Exceptions, https://www.cms.gov/ Medicare/ Prescription-Drug-Coverage/ PrescriptionDrugCovContra/ downloads/ 2011CoverageGapDiscount_043010v2.pdf)

Seeking reimbursement for in-network pharmacy purchases without using your Medicare Part D plan.
As noted in the Medicare Prescription Drug Benefit Manual Chapter 14:

"Although beneficiaries can still purchase a covered Part D drug at a network pharmacy without using their Part D benefit or a supplemental card, CMS encourages beneficiaries to use their Part D benefit. Use of the benefit affords beneficiaries access not only to the plan’s negotiated prices, which in most cases are the lowest price available, but also to the plan’s drug utilization review and other safety edits that only can be provided when the plan adjudicates the claim. Beneficiaries who choose to make a cash purchase will continue to be responsible for submitting documentation to the plan for determination of whether they are eligible for reimbursement and for costs to be included in gross covered drug costs and [total out-of-pocket costs] TrOOP.  Guidance included in section 50.4.3 below [of chapter 14] replaces CMS’ former cash purchase policy and clarifies plan processing of beneficiary -submitted claims for cash purchases as well as enrollee costs and amounts to be included in the enrollee’s gross covered drug costs and TrOOP. " [emphasis and links added]

(Section 50.4.2 – Beneficiary Cash Purchases (Rev. 17, Issued: 08-23-13, Effective Date: 06-07-10, Implementation Date: 1-01-11)) (https://www.cms.gov/ Medicare/ Prescription-Drug-Coverage/ PrescriptionDrugCovContra/ Downloads/ Chapter14.pdf)

We wrote about the CMS "cash purchase policy" in three different articles (2006, 2010, and 2013) - and as noted in 2013: "Previously, CMS permitted enrollees to purchase a covered Part D drug without using his or her Part D benefit or a supplemental card and have the cash price count toward the enrollees’ total drug spending and TrOOP. The policy applied if the enrollee could obtain a lower price at a network pharmacy than the plan’s negotiated price in any applicable deductible or coverage gap when the enrollee incurs 100 percent of the drug cost.":

• CMS Memorandum: Lower Cash Price Policy
  
• Lower Cash Price Policy: 2010 Update
  
• Lower Cash Price Policy: 2013 Update

A few notes about seeking reimbursement when you do not use your Medicare Part D plan to purchase medications:

As was noted above, the Medicare Part D program is voluntary and you are not required to purchase medications using your Medicare Part D plans.   But if you do not use your plan (e.g., you use a pharmacy discount card), the drug purchases fall outside of your Medicare Part D plan.

This means that if you have purchased your medications and did not use your Medicare Part D prescription drug plan, then the cost of the medications will not be counted toward your initial deductible (if any), nor will the purchase count toward your total out-of-pocket costs (TrOOP). The logic here is that your Medicare plan simply has no way to track such purchases outside of their reporting system.

So in past years, there was a provision that allowed people to submit their purchases for reimbursement and inclusion within their Medicare Part D plan. The rule behind this is called the Lower-Cash Pricing Policy and can be found here:  CMS Memorandum: Lower Cash Price Policy

But, in past years, Medicare has changed this policy and, as noted in the Medicare Prescription Drug Benefit Manual (Chapter 14, Section 50.4.2):

“Previously, CMS permitted enrollees to purchase a covered Part D drug without using his or her Part D benefit or a supplemental card and have the cash price count toward the enrollees’ total drug spending and TrOOP. The policy applied if the enrollee could obtain a lower price at a network pharmacy than the plan’s negotiated price in any applicable deductible or coverage gap when the enrollee incurs 100 percent of the drug cost. The enrollee was required to submit the appropriate documentation to his or her plan for the incurred drug cost to be included in gross covered drug cost and TrOOP.

Since the beneficiary cash purchase policy was issued, the Part D benefit has undergone significant change. Beginning January 1, 2011, the changes created by the Affordable Care Act (the ACA) started closing the coverage gap for beneficiaries not receiving LIS. By establishing the Coverage Gap Discount Program, which makes manufacturer discounts available at point-of-sale to non-LIS beneficiaries in the coverage gap, and gradually increasing coverage in the coverage gap for both generic and brand name drugs and biologics, the ACA for the most part has eliminated the need for this policy.

[As already noted above:] Although beneficiaries can still purchase a covered Part D drug at a network pharmacy without using their Part D benefit or a supplemental card, CMS encourages beneficiaries to use their Part D benefit. Use of the benefit affords beneficiaries access not only to the plan’s negotiated prices, which in most cases are the lowest price available, but also to the plan’s drug utilization review and other safety edits that only can be provided when the plan adjudicates the claim. Beneficiaries who choose to make a cash purchase will continue to be responsible for submitting documentation to the plan for determination of whether they are eligible for reimbursement and for costs to be included in gross covered drug costs and TrOOP. Guidance included in section 50.4.3 below replaces CMS’ former cash purchase policy and clarifies plan processing of beneficiary-submitted claims for cash purchases as well as enrollee costs and amounts to be included in the enrollee’s gross covered drug costs and TrOOP.”

In the next Section 50.4.3, the guidance continues and establishes that Medicare Part D plans will restrict the Lower Cash Pricing reimbursement model only to situations where no network pharmacy is available to the plan Member:

“CMS regulations and guidance specifically address the requirement for Part D sponsors to issue standardized cards that may be used by an enrollee to ensure access to negotiated prices under section 1860D - 2(d) of the Act. The only way that an enrollee can be assured access to the negotiated price at the point of sale is through online adjudication of the prescription drug claim. Therefore, to ensure access to these negotiated prices, the billing information on the standardized cards issued by the Part D sponsor must be used by the pharmacies at which beneficiaries fill their prescriptions to submit claims to an enrollee’s plan sponsor (or its intermediary). Thus, another price available to the beneficiary at the point of sale, for instance, the pharmacy’s “cash price,” would not be the negotiated price because it is not accessed by the use of the standardized card.

CMS encourages beneficiaries to use the Part D benefit, because generally it believes it is in the best interest of Part D enrollees to have their claims consistently processed through the Part D sponsor (or its intermediary). Not only does processing claims through the Part D sponsor ensure access to Part D negotiated prices, but it also ensures that proper concurrent drug utilization review (including safety checks) is performed (as required under 1860D - 4(c) of the Act). Only the plan can prevent payment to excluded providers or conduct accurate concurrent drug utilization review when a beneficiary uses multiple pharmacies. Online, real-time processing also facilitates accurate accounting for enrollees' true out-of-pocket (TrOOP) and total drug costs by the Part D sponsor so that each claim is processed in the appropriate phase of the benefit and accurate cost sharing assessed.

Guidance in section 50.4 of this chapter instructs plan sponsor s to process all claims online and in real time. The requirements of accurate TrOOP accumulations, Part D benefit administration of multiple coverage intervals, and coordination of benefits with other payers all necessitate online, real-time adjudication of individual pharmacy claims. This guidance states further that CMS expects Part D sponsors will establish policies and procedures appropriately restricting the use of beneficiary-submitted paper claims to those situations in which online claims processing is not available to the beneficiary at point-of-sale (such as out-of-network pharmacies) in order to promote accurate TrOOP accounting as well as to minimize administrative costs to the Part D sponsors and the Medicare program and reduce opportunities for fraudulent duplicative claim reimbursements.” [emphasis added]

You can read more from the Medicare Part D manual here: https://www.cms.gov/ Medicare/ Prescription-Drug-Coverage/ PrescriptionDrugCovContra/ Downloads/ Chapter14.pdf

For example:  A Medicare Advantage plan's Evidence of Coverage (EOC) document might note in the section: “When you buy the drug for a price that is lower than our price” (see, Chapter 7, Section 4.1) that you will not be reimbursed for the cost of your discounted drug purchases, but you can submit the purchase receipts when you are in the Donut Hole for credit toward TrOOP:

“Sometimes when you are in the Coverage Gap Stage you can buy your drug at a network pharmacy for a price that is lower than our price.

• For example, a pharmacy might offer a special price on the drug. Or you may have a discount card that is outside our benefit that offers a lower price.

• Unless special conditions apply, you must use a network pharmacy in these situations and your drug must be on our Drug List.

• Save your receipt and send a copy to us so that we can have your out-of-pocket expenses count toward qualifying you for the Catastrophic Coverage Stage.

• Please note: If you are in the Coverage Gap Stage, we will not pay for any share of these drug costs. But sending a copy of the receipt allows us to calculate your out-of-pocket costs correctly and may help you qualify for the Catastrophic Coverage Stage more quickly.“

Bottom Line:
You are not required to use your Medicare Part D plan when purchasing formulary medications at a network pharmacy.  But you may not be reimbursed for any of your costs associated with these purchases as it seems as though the former "Lower Cash Pricing Policy" has been eliminated (or limited to emergency out-of-network situations) so that more people will rely on the Medicare plan’s electronic record keeping system.  And you probably will not be able to retroactively submit your in-network claims to receive the Donut Hole discount.

Disclaimer:  Please contact your Medicare Part D plan or Medicare (1800-633-4227) for a further clarification.