If you really want you can keep your account offline, then just make a separate free online account that you log in to when you want to download a patch, then you would just login and load up the game and you will get a prompt for the updates. You'll surely get a prompt to update the dashboard as well, so I guess that's another concern, not sure how old your Xbox is but the interface has gone through a few stages of evolution though IMO not necessarily all for the better.
Then again if you're not online with it the interface doesn't really matter much beyond loading up a game. Getting the updates is a good idea, lots of games these days have 'day one' patches, which is pretty much admitting that they know they are shipping broken games.
Oh, one important consideration, do you have an Xbox model with a hard drive? Or maybe 4GB flash? I think some of the very early models were available with no internal storage. You'll need some space to download patches.