Can I verify an Xbox 360 game isn't damaged by installing it?

If I buy a used game the first thing I do is install the game onto my hard drive. I figure that this process must read the entire disc and so will verify the disc is not damaged.

Does anyone know if I'm right?

EDIT

ChrisF has seen games that won't play from disc but will install and subsequently play. That leads me to add another sub-question:

Has anyone installed a game successfully but then been unable to play it, either due to disc damage during the startup disc check or due to some other corruption?

I don't have a reference, but from personal experience I think you're nearly right.

If the disk is too badly damaged then you won't be able to install it at all.

However, it appears to be that the installation process is slightly more tolerant of damage than playing directly, so you could get a disc that's too damaged to play but will still install. This could be for a number of reasons including that it does more error checks and retries when installing than playing for example.

From personal experience there have been a couple of games that occasionally failed to load/play direct from disc. In these cases we have installed the games to the hard drive and successfully played them from there.

So your test won't verify that the disc is not damaged, but will verify that it's playable.

I do think that usually a disc with damage that affects the 360s ability to read it will not install successfully. A generally good way to test for damage, but it does sound like it isn't 100% reliable. If you have a big enough hard drive you might just want to keep it installed.