Yes. However, your monthly membership fee cannot be submitted to Medicare for reimbursement. You must sign a waiver every two years that declares that neither you nor your doctor will directly bill Medicare for your membership fee.
Medicare and medicare supplemental insurance will still cover medical costs that you incur outside of Equality Healthcare. For example, prescriptions that you fill at an outside pharmacy, or labs run at an outside lab, or hospital charges, physical therapy, x-rays and scans are covered, just to name a few. You do not lose your Medicare coverage for other medical needs just because you are a patient of Equality Healthcare.