No, once your Medicare Part B benefits become effective you have 6 months (including the effective month) to purchase a Medicare Supplement (Medigap) plan. This is your Medigap Initial Enrollment Period. You cannot be turned down by any insurance company offering a Medigap plan in your area.
After the Initial Enrollment Period ends, Medigap plans do not have an annual enrollment period like Medicare Advantage and Part D drug plans. You are not guaranteed the right to purchase a Medigap plan outside the Initial Enrollment Period in most states.
Medigap plans do not include prescription drug coverage. This requires a separate Part D plan. You are eligible to enroll in Part D the month your Part B benefits are effective and the following 3 months. After that, you can change Part D plans annually during the Open Enrollment Period.