What happend with Mandrake?

I could be facetious and say "I think he was that little wee fleck being blown into space in that second-from-the-last hydrogen bomb that went off at the end of the movie", but that wouldn't be nice.

However, it's not likely he nor most of the world's population would have gotten down to that underground sanctuary they were talking about in the War Room at the end.

In fact, it's more likely even those underground sanctuaries wouldn't have gotten up and running in time, given the complexity of the problem and the short amount of time before the Doomsday Bomb did it's trick.

Since they manage to recall most of the bombers except for Major Kong's, we can assume that Mandrake managed to get the code out and since proved he wasn't a part of Ripper's plot. Whether it would've gotten him a spot in an underground shelter is up in the air, I can only imagine Mandrake would've preferred to return to Great Britain before the Doomsday Machine took effect.

If the other Americans were as stereotypical as Col. Guano (which if you look at Gen. Turgidson wouldn't be totally out of the question) then we can assume that neither they or the fascist Dr. Strangelove would've taken special care to save a Brit like Mandrake, despite coming from an allied country and helping to stop Ripper's attack. If the British decided to adopt an underground shelter plan like the Americans then perhaps Mandrake would've survived but it's unlikely, but then again everyone in the movie is almost certainly doomed.

Can't be too careful with all those weirdos running around.