Maybe slightly, over time..? But I think, at least for me personally, whether or not I get affected by a certain fictional narrative 100% depends on whether or not it stirs something in me, emotionally. If I read a book, play a game or watch a movie that's just sort of "meh"..? Then it usually won't change me very much at all. Whereas if I'm subjected to some sort of storyline that deeply touches me, at a soul level, by making me feel all sorts of things..? Then that becomes a part of me, to the point that it often teaches me a lot of profound lessons, about life and this existence as a whole.
And the thing is... I've yet to be deeply emotionally touched, or reached, by any sort of 1st person shooter game! It's just a whole lot of mindless violence, that doesn't really mean anything at all.. So it just doesn't feel REAL to me in any way! Which is why it has not affected my views on, and relationship with, death, even in the slightest....
So there you go, that's just my experience. Although it's probably not everyone's experience, though.. Seems like a lot of boys, and men, can get completely IMMERSED in 1st person shooter games, to an extent that has just NEVER happened to me, because I rely so much on plot/narrative and emotional resonance... I'm just generally a VERY emotionally driven person, for what it's worth.