If a burned 360 game has an update available via Live, will it potentially hurt to download it?

I recently flashed the LT+ to my 360's DVD drive and have played a few burned games with no trouble. I went to play Forza 3 though and upon starting the game, it said there was an update available for it. Is it safe to install updates like this one? Could it potentially tip off MS that my console is modded and get it banned? I don't know what the update is for, but I probably don't need it anyway. Not installing it just prevents me from playing the game online or downloading new content for it, which doesn't really bother me. I only have a Silver Live membership anyway.

On that note, if my console gets banned, does that mean my gamertag or other gamertags associated with the system get banned too? Should I create a separate live account for use with my burned games just to be safe?