Given the slip stream, I don't think Major Kong would have been able to stay on the bomb as he rode it down
I don't know about hanging on to the bomb, but I'm pretty sure he wouldn't have been able to hold on to his hat
I love that movie - there are a few of us at work that often quote lines from the movie. Just saying "Now Demetri" is often enough to break the tension and start the laughter.
BTW, a little trivia for you - when Kubrick started making the movie, it was intended to be a serious movie (not unlike "Failsafe", which came out at pretty much the same time). But as he got into the production, Kubrick apparently decided he couldn't do it as a serious movie and changed it.