There's no real reason why Rockstar couldn't make a game with multiple protagonists and have one of the characters be a woman. There are of course plenty of women involved in crime at all kinds of levels. Even the clichéd crime movie tropes that GTA works best with have plenty of examples of women in crime fiction. There is the popular 'hooker with the heart of gold' or the 'schemer' or the 'gangster's moll' archetypes that they could easily work with, and that's without even getting in to the realms of reality.
This could also potentially garner more interest from women in GTA, although that's highly speculative of course.
It wouldn't work though if a woman was the only lead character. Primarily because we aren't used to seeing women performing the kind of actions that GTA protagonists do, and GTA is a game that has always played upon popular social concepts and Hollywood tropes. So the gameplay would have to be different, which would have a negative effect if a woman was the only playable character.
Also, most of the current GTA gamers are male. Sure it's one thing to watch a movie or even read a novel wherein the lead character is a woman, but in a game it's slightly different. The need to identify with a character in a game is slightly different. To a certain extent, a game avatar is an extension of the self, through which your actions and agency are represented. This is why when you tell your friend about something that happened in game you would say "I jacked a cop car" this is because it's your actions that are represented. You wouldn't say "Niko jacked a cop car" because you aren't just watching a character do something, you are assuming the role of that character and your identity is represented to a certain extent through them from a psychological perspective.
That's why most men find it slighlty more difficult to identify with a female character. That's why if you have the choice of character on any game, most men will make a male character, although i'm sure that social convention plays a significant part in this too. men typically will feel more comfortable playing as a male avatar.
So yes, having a woman as one of multiple characters could work just fine. But having a woman as a sole lead would be a mistake i feel...
Oh yeah and of course girls are stupid and have cooties etc...
Look at the character Michelle Rodriguez plays in the Fast & Furious films. Now that's a female character that would fit well in the GTA world.