Here is my take on this question, and while I hate to disagree with the position Edward takes because this is one of those extremely heated debate issues, yes, I believe homosexual tendencies can have a biological component to them. I once read that a Russian women's Olympic team (gymnastics, track, luge, so help me God I can't remember now) got disqualified because it was discovered they had been so pumped up on testosterone injections that it had even started changing their anatomy.
Can't find a link to that now, but the Russians still engage in this somewhat, as the following stories relate:
Whistleblower Yulia Stepanova has denied being a traitor and said being banned for two years was the turning-point that led her to expose Russia's state-backed and systematic doping programme.
www.reuters.com
www.watchathletics.com
The interesting thing is, the Olympic committee now recognizes that a difference in testosterone levels among some women gives them an unfair advantage, so even women with naturally higher testosterone face the potential of being banned now, which I find makes the whole transexuals allowed to compete in certain sports rather hypocritical, but such is the world of political correctness nowadays.
Here's the thing. Can God heal such people? Yes, I believe He can. Even if it is a purely physiological problem - and I know a woman who works at a convenience store nearby who takes hormone shots to be more masculine physically - I believe such physical effects can be healed, just like any other physical condition can. But to receive healing does indeed require faith, for as scripture says, even Jesus could not do many miracles in his home town because of their lack of it (Matthew 13:58).