Troy, Brexit will happen or it won't, and if it does it could be what's being pimped by the various parties or a mishmash or something completely different. After two years not even those involved in the deeper process know the outcome. While the UK's ongoing farce will pan out eventually, in or out we are inextricably linked to the EU through proximity and a common social and economic mindset, which is why the Brexit chaos and whatever it results for the UK is the lesser event that pales into insignificance against the impact of a failing EU.
I don't expect everyone or even many to see it this way, esp since most people seem to accept the EU as a permanent fixture like the thousand-year Reich, but wishful thought isn't going to pull it through.
Will she resign if the vote goes against her? Could be yes or no, with the current state of play being gross uncertainty.