Actually, I have this long, overly complicated, and maybe childish way of always projecting myself into the shoes of the protagonist, regardless of who they are.
When I was 9, really getting into gaming with my N64, I was playing Ocarina of Time imagining what it would be like to actually be there. I'd dream about it sometimes, it was one of the first games I played that allowed me to explore so openly. But then I realized, the game itself was my way into the world. So I started playing pretend AND video games at the same time. I would sometimes talk out loud to myself as Link, (mainly in my own head though to avoid looking insane..) and I would create my own narrative outside of the one already existing in the game. "How did I get here? Who am I?" I'd look in the water, though there werent water reflection in Ocarina of Time, and say to myself "No way...I'm Link!" and then play the entire game with that mindset.
As I got older, the narrative I created for myself got more complicated. I even created for myself one, large antagonist. "The Game Master". A huge, evil entity that controls all games, on all platforms, of all genres, for all time. With his power, he is able to literally transfer a persons existance into the digital world, forcing them to fight in these video games for their actual life. Depending on what game they were sucked into, they could either die immedietely, or have a few chances at death, if the game rules apply. (you can also earn more lives, and these earned lives are transferable to all games). Thus, "I was warped into the digital world". My first game was Grand Theft Auto 3, the first game I used this larger narrative for myself. No matter the graphical quality of the game, as soon as you were warped into it, it all looked real (with a few exceptions, such as overly colorful games still looking real, but obviously with exaggerated color), so I thought the world of GTA3 was just a real city that I somehow been transported to. I "slowly found out how real, but unreal everything really was, and that the only way to return home was to complete the game as if it was my destiny in life".
I pretended main characters of games were once real people, who have been trapped in the game by the Game Master, forced to be in here for all enternity until they can find the way out. All main antagonists of games are actually working for the Game Master, trying to torture and kill people for the enjoyment, but also because that data of death becomes power for the Game Master. Eventually I became what was known as an "Elite", one of the few people sucked into the digital world that can temporarily return to the real world, but will soon have to go into another game to be faced as a challenge. A 6 hour game to just a normal gamer can actually be several days, or weeks, or years to someone in the game, but my real body will never age, only my digital one.
There are times when I'm not the actual character, but rather temporarily being a part of their body to give them the power to press on so they can escape from the game.
All abilities and powers I gain in a game cannot come out with me into the real world, so no matter how many computers I expertly hack in Fallout 3, I forget all knowledge of knowing how to hack once I escape the game. No matter how strong I got in Skyrim, it is back to my average body in the real world.
So, as you can see, I have built my own story to go along side the actual story of the games I play, and I've been doing this since I was 9. I'm 19 now, and as a habit I still think about these things, but I don't think about it nearly as much as I did when I was younger. Still though, it's actually made my experience with games more immersive, and more fun, even with bad games. It doesn't matter what gender, sexuality, race, or religion the main character is, that is the body the Game Master has given me to fight with, and it also challenges my understanding.
I actually plan on writing a book about this, more fleshed out and detailed. I think it could be a great book about gaming that we need. Sure, it's not about gaming itself in the real world, but it's about being a part of those games.
So to finally answer, yes, I typically always immerse myself as the main character, regarless of who they are.
