If she were the VP nominee, her alleged affair would get heavy scrutiny. She'd probably refuse to be vetted if it's true and I'll say it is, going only off the fact that she's from South Carolina, home of Mark Sanford, Strom Thurmond and Lindsay Graham.
Given the wording Gov. Haley has used when rejecting accusations that she cheated on her husband in the past, my personal guess is that she has an open marriage. It's not exactly something new to the US, although being completely out of the closet about it rather rare, and open marriages are probably a small percentage of the population.
If that's the case, I think it would be great to see a pro-open marriage candidate. But it would probably be the kiss of death to any Republican politician, or any politician from either party running on a national ticket.