actually, it does (at least under current definitions; i don't know what it was like during Churchill's lifetime, but the definition of "natural-born citizen" extends to the children of one or more American citizens, even if they were not born in the United States themselvesFirst, Churchill's mother's nativity would not make him eligible for the presidency. It would be if he was born here. So, one aspect of his presidency would be moving the whole "birther" thing up a few generations earlier.
if anything, Churchill would get flak for being born in England like George Romney did for being born in Mexico, with the difference being that Churchill is a much more credible and capable politician