I actually remember reading an article by some science types on the authenticity of Indy's hiding before.
They actually seemed more concerned with how they depicted the mushroom cloud and the explosion, apparently it was wrong for the type of bomb they used.
Also that as it was a small yield bomb, detonated underground and not directly on the town, he had at least a slight chance... however, the second he steps out of it he is exposing himself to stupid levels of radiation... which is where it gets pretty silly.