If you sign up for a Medigap plan when you turn age 65 and have prior creditable coverage, your plan is considered guaranteed issue and will cover pre-existing conditions.
Medicare Part A and Part B does not have a pre-existing clause so even if you lacked prior creditable coverage you still have full coverage under Medicare.
Yes, a Medigap policy will cover all of your per-existing conditions, as long as a portion of your treatments are covered by Medicare. This is one reason it is s important to enroll for a Medigap plan when you are first eligible, when coverage is guaranteed issue. If you try to apply outside of an open enrollment period, and have pre-existing health problems, you can be turned down for coverage. Like other types of insurance, you need to BUY NOW, before you need it, so coverage will be available when the time comes that you have a need.
Medicare Part A and Part B does not have a pre-existing clause so even if you lacked prior creditable coverage you still have full coverage under Medicare.