sunflower

It depends on the fandom, for me. I only read fanfics based on games I've played, and I prefer them to be fairly consistent with the way the game set-up without going so far as to be a complete rewrite. If it's based on something like Tales of Symphonia, where there's a fixed number of characters, a set leader and you don't create a player character, it feels like a self-indulgent intrusion suddenly having a new one turn up just so they can smooch their favourite character.
If it's based on a game like Hordes of the Underdark it's a different scenario. There you create the player character and have a strictly limited number of henchmen, one of whom (possibly two with if it's a male character) has the potential to romance your character. In that case, I fully expect to see an OC in a fanfic related to that game and it doesn't come across as jarring - I'll evaluate it from there based on how they portray that character. The story would have to be changed pretty radically to avoid that scenario since the player character is really set up as entirely central to the story. Same with Neverwinter Nights 2, only there are more companions around.