Yes, you can, especially if you join during the Medigap Open Enrollment Period. This is a six-month period starting on the first day of the month you turn 65, and you're enrolled in Part B. During this time, you cannot be denied a Medicare Supplement plan, no matter your medical condition.Yes, you can, especially if you join during the Medigap Open Enrollment Period. This is a six-month period starting on the first day of the month you turn 65, and you're enrolled in Part B. During this time, you cannot be denied a Medicare Supplement plan, no matter your medical condition.