It depends how badly damaged it is, if its not too bad it might install OK. But even if it does there is no guarantee it will boot up off the disc.
Do you have a friend with a 360?, you could try it on their HDD to make sure it will work before buying onr yourself.
Have you tried getting the disc buffed at a game retailer?,if not its worth a try and it does not cost much.
Alternatively if you buy a HDD and the game wont install rent a copy and install that, then hopefully (again if your disc is not too damaged) it might boot up.
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