Faulkner was a great writer. Of course in the 1930s he couldn't come out and say it point blank, but he left us clues.
He says outright that Homer "liked men" and "was not the marrying kind." Then there is his name, which sounds like "homo", and the fact that Emily was obviously an asexual person. It's hard to imagine her taking a man into her life for anything else other than companionship.
Of course Faulkner leaves it up to the reader to decide, but I vote yes.
There's no absolutely obvious reason to believe that he was gay, though you could interpret one or two remarks that way. The story was published in 1930, and Faulkner could not, at that time, have openly stated or even clearly implied that Barron was gay, but he does leave a number of questions unanswered and therefore susceptible to much speculation.
I don't think so