I don't know if it will. I don't thing TGA is woke-leaning politically speaking, I could be wrong and maybe they are. There have been a enough Nintendo nominations and awards that I feel like they are fairly center, politically speaking, considering Nintendo games are about as anti woke as games can get.
I mean, so far, The Last of Us Part II and Hades are neck and neck in regards to winning GOTY honors. With the only other games receiving honors being Ghost of Tsushima and Final Fantasy VII.
Furthermore, I find it ridiculous that if TLOU2 wins or even loses Game of the Year, it's becomes some sort of a political statement instead of a regard of the quality of the game based off your comment.
This coming from a person that wants Ghost of Tsushima to win GOTY and played Animal Crossing more than any other game this year...