BINGO. if you boot the game while connected to xbox live and it DOESN'T PROMPT YOU TO UPDATE, then it has already done so in the background. (the update is a new version number of the game and even though this is invisible to us, the end users, the game will not allow an old version while connected to xbox live)
unless you go offline to play, this is the surest way to know you are patched. the game will not let you play w/out prompting you for the patch when you are online -- unless you already have it.