Dungeons are not to be confused with strongholds, which are entire underground complexes containing portals to another dimension.
Can a stronghold contain a dungeon? I've never found one so all my experience is theoretical.
Probably, I think they are generated at the same step as abandoned mines and ravines. If those can get dungeons there's no reason strongholds can't. Of course, since strongholds are extremely rare in comparison the chance of actually encountering that situation is going to be very low.