None of the shit birds we've had in living memory would, with the possible exception of Carter. Bush the senior might surprise us though; he was a fighter pilot who saw action, after all.
Clinton would definitely take the pod, but Hillary would stay and kick ass, though, 555. I agree with Sam's list, and would argue that both Roosevelts would stay behind, although I'm not sure Franklin could do much in the way kicking terrorist ass (same same for peanut farmer Carter). Teddy though, for sure.
Truman would, he was a scrappy guy by all accounts.
Jefferson would too, I think, although again, not a noted pugilist. Ole "Tippecanoe" Harrison most definitely would. U.S. Grant, maybe, if he had his liquid courage up. Of course there were no such thing as airplanes back in their day; maybe they'd have to stay and fight the terrorists who were taking over the Presidential Airship.
Of course the ultimate in Presidential Bad Assery was Chester A. Arthur: