Gender may not be as important to immersion as one might think.

I'm equally immersed in Portal and Half-Life, even though the main characters are of different gender. However, I don't see them on screen much.

I am immersed in Metroid games, whether its 2d or 3d, but not immersed in Other M because the game has poor flow and feels intrusive with story.

I get immersed in a good MMO whether I am playing my male or female character.

Immersion has a lot to do with cohesive elements. How directly connected the player is to what the character does, how well the world around them is built and feels alive, how well the audio works in establishing a setting, and how much the mechanics give a sense of 'I do', 'I grow', and 'I feel'.

Character wise, the silent protagonist is probably easiest to be immersed within, but so is a well written character. Least immersive are characters you don't like or would avoid in any other type of fiction based media.

I was never connected with the main character in GTA Vice City, because I felt like I was just a criminal asshole. I felt a bit more connected with CJ in San Andreas because he felt like he was coming from a real situation. I struggle still with GTA games since I don't have a chaotic streak in me that enjoys rampaging through modern society. I always felt the fact that the worst that would happen to me is a trip to the hospital and some loss of money made the whole situation a joke.

For these reasons, I was more into Red Dead Redemption and Sleeping Dogs. The setting and situation are different. The Wild West as a place where the law is not always the law? Okay, I can buy that. An undercover cop in Hong Kong? I play both sides? I can feel that situation.

I just can't identify with being a mafia douchebag in Miami, killing everyone and having nothing of consequence happen to me.