Regardless a movie about him could be fascinating. Granted also that many would claim it either whitewashes him or demonizes him. It would literally be impossible to make a movie about him that everyone agrees is an accurate portrayal.
While Hoover was an odd duck, I believe he tended towards asexuality rather than homosexuality. There were too many people that hated him, and considering he busted several hundred Mafia guys, if the photos existed, the mob would have used them.