No, the hard drive cache on the 360 is about 16MB or so. And each update is about 4MB, so if you updated games prior to New Vegas the cache will clear space for that update.
Say if I put in GTA IV and was prompted for an update and the the 4th most recent game I had in was Left 4 Dead. Than the update for Left 4 Dead would be dumped because I just added a new game to that line up. If you look at the dashboard you'll see it shows the 4 most recent games you have played. That actually has relevance towards which games are 100% ready to be played with no update required.