I think quantum mechanics and the MWI are a red herring here. The real question is whether you can compute the probability of counterfactual events like WWII not happening—and as Viliam says, the answer to that question is that it depends on choosing a starting point in the past to diverge from. Of course, once you choose such a point, actually estimating the probability of WWII not happening is an exercise in historical reasoning, not quantum physics.
I think quantum mechanics and the MWI are a red herring here. The real question is whether you can compute the probability of counterfactual events like WWII not happening—and as Viliam says, the answer to that question is that it depends on choosing a starting point in the past to diverge from. Of course, once you choose such a point, actually estimating the probability of WWII not happening is an exercise in historical reasoning, not quantum physics.