Will an FBI medical background check reveal my HIV status? How?

I'm not certain about what you are speaking of regarding an FBI medical background check. Generally potential employers do ask applying parties to undergo a medical check or at least fill out some medical information. That is not illegal.

I do not know the answer to your question. I do not know what resources the FBI uses to do a background check. I am not familiar with this term: medical background check As far as I know, there is no central data base on health issues that is available to any one but medical professionals. If you are not asking about a physical relating to a job at the FBI, you are likely confused as to who does medical exams.