Doubtful. In otb, crazyhouse is played at blitz speeds, and is normally enjoyed as a way to use intuition more than worrying about calculation. As far as possible number of games, it likely to be over 10^240, or 10 followed by 240 zeros. Still a paltry fraction of go positions though.
But since it's usually played at a fast rate, there would be little reason to study a crazyhouse game afterwards.
hm?