Hmm well, I think it would have been believable and she would have been a serious contender among the other serious contenders-nominees for the award. I don’t think she would have won though. Like I said before, the GOT nominations pretty much tried to bring young viewers to the award show, but it’s nice when popularity matches talent, like in Diana Rigg’s case. GOT is a popular show, with a large viewership, that brings viewers excited to see their favourites at the award show, and surely a lot of press. So, nominating actors and the show in general brings that attention, but for most of the nominations, including acting, there was no talent or merit, but just character popularity and trying to secure some good ratings. Fairley's nomination wouldn’t have brought the award for the show, but it would have been a serious and believable nomination. I think Rigg had more chances to win than Fairley (if she had been nominated).
It's hard to answer this question when I haven't watched all the other performances nominated, especially the one of the actress who actually won. Do I think Fairley had enough talent and a great performance to compete? Yes, I do. Do I think she could have won? I don't know. I think her performance would have gone neck to neck with Christine Baranski's (The Good Wife), and it was easily above Morena Baccarin's (Homeland). But I don't think it could have upstaged Maggie Smith's. About Christina Hendricks' and Anna Gunn's, I can't say much or compare the situation, because I don't watch Breaking Bad, and I haven't regularly watched Mad Men in a long time.