You’ll need to plan accordingly. Airlines are prohibited from allowing passengers with a positive COVID test. When applying for AP, you’ll probably need to request a buffer in addition to the amount of time you’ll be out of the country. If you are applying for multiple entry AP, that may be easier since it doesn’t limit your entries to one and you could have it for a longer period of time.

On the CDC website, it does allow for someone to have a positive COVID test to present a letter from a Doctor clearing them for travel