With all these responses, I'm noticing something.
If you said, as long as the character wasn't gay just because:
Most characters are heterosexuals just because.
If you said, as long as it was pertinent to the story:
Being heterosexual is almost never pertinent to the story.
And one person said that being gay makes a hero not as badass:
Let's say Master Chief was gay (I'm gonna get murdered for that) and that not once in the game did it ever mention he was gay. But then the creators came out (a la J.K. Rowling and Dumbledore) and said he was. Would that make him any less badass?
If a character is badass, they're badass. Whether they end up kissing their female or male interest in the end is irrelevant to that.
Personally, I think all characters should be asexual (if it's a game that doesn't allow romance as an option, like the BioWare games).
Sexuality/sexual orientation shouldn't be the character. If any game makes a point of forcing a character into a sexual situation (without choice) it's just unneeded.
Albeit there are exceptions, such as Indigo Prophecy (where the sexuality adds another layer to the characters) or God of War (where his heterosexuality is important because of what happened to his family, although the gratuitous sex scene was just obnoxious).
To answer your question, I would.
As I said, sexuality/sexual orientation shouldn't be the character. It can be used as a layer in the character's personality, but too much of it is just painful.
And to be honest, I doubt we'll see a gay player character (who was built from the ground up to be gay). The action and shooter games are getting less and less character and story driven while the RPGs are getting more player choice based (as those are the main genres to use character's to their full capacity). The only game I see that would ever come close is GTA. And that game is stuck so far up it's own THIS IS WHAT MEN ARE! ideal that it'd never portray a player character as a gay man.
Especially when the one relatively deep gay character they created was still quite stereotypical on the surface (the pink/purple glasses, running nightclubs, partier, etc.).
Yeah. This is my first real post. I thought I'd make it count. xD