Would Installing a Clean Copy of a Game to My Xbox 360 Play a Badly Scratched Copy of the Same Game?

So i was playing my brand new copy of battlefield bad company 2 yesterday and my niece ran into my xbox while i was playing, causing a loud grinding noise. I took out the disc and a huge circle scratch was on the back. Possibly a laser burn. When I put it back in, the xbox recognizes what game it is but it tells me the disc is unreadable when i try to play. My brother has the same game as well, so i was wondering this… If i installed his clean copy of the game onto my xbox would i be able to play my scratched copy after wards?

Suggestion:

As long as the system can read the copyright information from the disk (only requiring the disk to spin and read for the first few seconds), then you will be able to install another disk of the game and use your damaged one to play the game.

Tagged as: how to copy my battlefield bad company 2 to my xbox 360, install a clean copy game on xbox 360, install clean copy play with damaged disc 360