Circular Scratch on Xbox 360 Game, Can It Be Fix by Installing It?

so my game has the circular scratch on it. s my disc still works but you cant do some of the things u can with a normal one .if i borrow or rent a game and install it to my hard drive, will it still play even though i put my broken disc in?

Suggestion:

yes it will, but as long as it can still read the disc, i woud'nt install the game fast before it gets worse