Short answer: Usually not in full. Retiree coverage pays after Medicare, and it may not pay medical costs for any period when the person was eligible for Medicare but didn’t sign up, so most retirees need both Part A and Part B.
Medicare is primary once employment has ended, whatever the size of the former employer. Many retiree plans pay as if Medicare paid first, which can leave a retiree without Part B owing most of the bill (the ERS HealthSelect Secondary plan, for example, says the retiree owes the 80 percent Medicare would have paid). Retiree coverage also does not count as coverage from current employment, so it does not protect against the Part B late enrollment penalty.
Before joining a separate Medicare drug plan, check with the retiree plan: Medicare.gov warns that enrolling in Part D can cause the loss of retiree drug and even medical coverage for the retiree and dependents, and it may not be possible to get it back. The plan must send a notice each year saying whether its drug coverage is creditable.
Ask the plan administrator for the summary plan description and exactly how it pays with Medicare before making changes.