Yes, by authorizing both computers with your iTunes account. And don't sync apps from both computers. Or music etc... One computer can sync an item, but they both can't sync the same item.
This is just a theory, but I think it'd be possible: 1) sync with the different computer, but don't sync apps, and check "manually manage music and videos". 2) use the owner of the computer's account to download apps directly onto your ipod 3) do the opposite of what you just did to get your account back on the device. 4) you should have the new music and apps, but I don't think you'll be able to keep the apps after the next sync.
****ing Linux won't even let me install iTunes. :L Stupid harddrive failure; I need a new harddrive nowwwwwwwwwwww