Androgyny is something that allows both genders to be equally adept. I don't think the gender of the actor is the critical element. In my mind, the question is whether or not they can capture that vibe that Boy George exuded in the mid 1980s. When he dances to "Karma Chameleon" or gives that distinctive wink at the camera in the video of "Time (Clock of the Heart," it seems that he developed his own style that many others tried to appropriate. The dance moves, the panache, and the overall charisma he exuded are real difficult to duplicate. The gender seems secondary to capturing these elements.
This really depends on the person, but it would be better if a guy impersonates Boy George. The most obvious reason for this is because Boy George is a guy, who dresses like a girl. So, to keep that cross-gender effect would be best as long as the impersonator was a male. In fact, in my opinion, that is part of the total package or persona of Boy George. However, there is a big caveat. If the guy can't sing or dance, then he would be a horrible impersonator. In this case, a girl would be far better as long as she has talent.
Personally, I can imagine why it would matter whether it was a girl or a guy impersonating Boy George. I would think that all that would matter is whether the impersonator had Boy George's moves down -- whether they would actually look like him when they were dancing.
After all, when Boy George was in his heyday, the stuff he wore did not really make it clear as to whether he was male or female. The clothes were pretty baggy so it didn't matter.
So if I were the one trying to cast the part, I'd just watch the people dance and decide who could imitate him best.