It can, if it's done well in an honest, natural way, if it wasn't just put there to fill a checklist.
However, the problem I think is that we've had so much SJW stuff thrown in our faces for a while now, that we might now think twice about it when we see it, while we wouldn't have in the past.
For example, I started watching Fear the Walking Dead years ago, but I stopped for various reason a long time ago, and I started again recently, by watching everything from the beginning again. One of the characters is black and gay, and I completely forgot about the fact that he was gay, because I just don't care, it's not a negative or a positive for me, he's just gay, and he happens to be black, fine, I didn't think about it back then. But now, when I rewatched it in today's climate, I did, unwillingly, had a thought about it like "uh", wondering if it was put there just to respect some ratio. It doesn't change the fact that he's my favorite character, but it created this small thought.
I think that SJWs are pushing some agendas so much, that it's actually doing the opposite, they are creating whatever "phobics" because they've been annoying people so much with that, while people were just fine / didn't care about it before.
I know that it's also not the right logical reasoning to have, I'm aware of it, but it's hard to help it when people constantly tell you "black black gay gay trans trans" all day, it's making all of it seem less natural. I think SJWs are actually doing the exact opposite of what they are trying to do, they are pushing people away from the things they want people to "accept".
People now, myself included, might feel like something risks being woke when it's not, just because it has the stuff we're used to see in woke medias.
Because of all of this, I think the reasoning and logic behind saying if something is woke or not is completely biased, and it's sometimes hard to tell.
My final thoughts though, yes you can have "representation" (although I hate that word because it just seems purely marketing), in medias, it just needs to be there naturally, not feeling forced. I just think that it should not be there to be a REPRESENTATION, it should be there because... that just exists and the author wanted to have this in their creation. The problem is when people think that everything NEED to have representation.
I think SJWs just ruined natural "representation" of things.