When you install a game on your HDD you only need the disc to start the game up. So once it is installed it will boot up using the disc and then switch to the hard drive once it is at like the start menu. So it would work but if the game is scratched it might not fully install.
You can try to borrow a friends MW2 and install it onto your HDD and then just use your scratched disc to boot it up. That WOULD work.