Bughouse falls in a different class, because it is a 4-player game, and is more comparable with Bridge. ThreeCheck and King of the Hill are not so interesting; they throw away alot of interesting aspects of orthodox Chess, such as late end-games, without giving anything back. Crazyhouse is a fatastic game, though. Nearly as good as Shogi. Playing orthodox Chess would indeed not do much to master it well.
Yet playing Chess is not completely useless. It definitely helps to improve your Chu Shogi skills.
I think Bughouse and stuff don't help you in chess, it is fun though but I mean it is just kinda dumb... It isn't that related to chess, you can win in some kind of dubious way like checking your opponent. It completely messes up your chess level. When you are playing a chess game you might start thinking about 3 check and start checking your opponent or just playing a crazy house opening when it is a real game.