Apparently, people with too much time on their hands have been:
Potter readers on fan sites and elsewhere on the Internet have speculated on the sexuality of Dumbledore, noting that he has no close relationship with women and a mysterious, troubled past. And explicit scenes with Dumbledore already have appeared in fan fiction.
This isn't the article by the guy who was lamenting that Dumbledore isn't much of a role model for homosexuals: he stays in the closet, abstemious, near as we can tell, until, long after his death, his creator outs him. The Pope couldn't have asked for better.
I like this, though, "Rowling...also said that she regarded her Potter books as a 'prolonged argument for tolerance' and urged her fans to 'question authority.'"
They are that. And do that.