No, unless you can somehow share an account. Actually, my brother and mom managed to do this with two 8GB 1st gens once, but I don't really know how. It was a while ago.
But then when he switches it to his own account the iPod will refuse to sync and backup the music. You can use music recovery apps, though, or jailbreak the iPod, to get some of the information off the iPod, but it would be easier just to use a thumb drive to copy the music over to the other computer (but just as legally hazy ).