Will Installing a Game on Xbox Prevent the Game from Being Played on Another Xbox?

Me and my brother both have our own xboxes, and copies of mw3. for reasons unknown, my xbox has scratched the disk, in a perfect circle close to the edge. my xbox can read the disk and tell it is mw3, but when i play certain points of the game, like multiplayer, it stops me and kicks me out of game because the disk cant be read. What i want to try is to install my brothers copy to xbox (it cant read mine) then give it back and put mine in. that way it will read the disk and confirm i have the game, but then play it from hard drive. my question is, will installing my brothers copy of the game prevent him from using it on his xbox, (i am thinking it might have some code on the disk or something that will only let you play the game on the system it's installed on) or no.

All that will happen is that you both get to play MW3 with no worries. Think about it, if installing the game prevented it from working on another console, a hell of a lot of pre-owned games wouldn't work and MS wouldn't hear the last of it.