Time Machine backups aren´t the best way to do this, but I suppose it is possible to mount them and get the files for a different machine, but I´d be somewhat cautious.
Anyway, as deauthorization works, you can keep the files on the other computer, you just won´t be able to play them there. Unfortunately you can just deauthorize all your computers at once and reauthorize them one by one. And you can´t deauthorize again for (i think) 6 month.
So if everything else fails. Put the backup back to the core2duo and copy the files from there.
Oh, and yes. Apple authorizes the machine. Not the iTunes library, so you have to authorize the new/old machine no matter how the files arrive there. The scheme has the benefit, that any user on the mac may play the files.
