HMMMM. I think it's likely, if only because of how hard she is to please so much of the time-- she was never going to be able to completely obliterate their ties (especially Mai's) to Zuko/the Gaang's side, and I think that no matter what one or both of them would have done something that she would have seen as a betrayal the way she saw the Boiling Rock thing as one. If by some miracle nothing like that did happen, though, I still think she would have "cracked" if she lost the war, just like she did in canon. She's so obsessed with war, and with the Fire Nation, and with winning and being "the best"-- even without the perceived betrayal of her friends, I can't see her taking a loss that big very well at all. She might not be ridiculously paranoid or terrified that everyone would betray her if she allowed herself to trust them, but other than that... yeah.