Oh...nope. Just on the desktop. ^^;
Lovely, it's easy then.
If/when, you put a newer game into the console, it'll ask you for an update. If you don't have the newest update, you won't be able to play games.
(You'll get an error code appear.) If your 360 isn't connected to the internet you'll have to download updates from the computer, and either
1. Burn the update to CD/DVD
2. Add the update to a USB stick.
It's all pretty easy to do. I can't get updates anymore from the official 360 site, so i've found another forum where you can download them (and they post a handy tutorial).
They new update (released 7th dec), was to prep the console for TV channels and apps (although to watch tv in the UK i thought you had to have a TV license. :S) and something to do with Kinect (basically, it's something that's of no use to me, but it's more than likely to be a mandatory update.)