No. COBRA continuation coverage does not count as creditable coverage that lets you delay Medicare Part B without a penalty. Medicare only allows you to postpone Part B penalty-free if you have coverage based on current employment, either your own or a spouse's, through an active employer group health plan. COBRA is coverage you get after employment has ended, so it does not qualify, even though it technically continues your old employer plan's benefits for a limited time.
This is a common and costly mistake. People leave a job, elect COBRA to keep their familiar insurance, and assume they can wait until COBRA runs out before enrolling in Medicare. In reality, once you stop active employment (or your spouse does), your Special Enrollment Period clock starts ticking. You get an 8-month window to sign up for Part B that begins the month after employment ends or the employer coverage ends, whichever comes first. COBRA does not extend or restart this window.
If you let that 8-month window pass while relying on COBRA, you will likely face two problems. First, you may have to wait for the next General Enrollment Period to sign up, which can mean several months without Part B coverage. Second, you will likely owe a Part B late enrollment penalty, an amount added to your monthly premium for as long as you have Part B, based on how long you went without creditable coverage after you were eligible.
There is also a coordination-of-benefits issue even during the window when you still qualify for the Special Enrollment Period. If you have COBRA and are also eligible for Medicare, Medicare generally becomes the primary payer and COBRA pays secondary, which means your COBRA plan may pay much less than expected if you do not have Medicare in place. Some COBRA plans will not pay claims at all for Medicare-eligible individuals who delay enrollment, leaving a serious coverage gap at the exact time medical bills are coming in.
The safe approach is straightforward. If you are turning 65 or already past 65 and leaving a job (or your spouse's job) that provided your health insurance, enroll in Medicare Part B during your 8-month Special Enrollment Period regardless of whether you also elect COBRA. You can use COBRA to cover things Medicare does not, such as certain dental or vision benefits, but do not count on COBRA itself to delay your Part B start date.
Before your employment ends, contact Social Security or your Medicare plan administrator to confirm your enrollment deadline and get written documentation of your group health coverage dates. If you already missed the window and are relying on COBRA, talk to a Medicare counselor through your State Health Insurance Assistance Program (SHIP) as soon as possible to understand your options and minimize penalties.