Q: using apps when deauthorized

I do not understand what you mean by iPod being deauthorized. Computers are authorized for iTunes accounts.

iTunes Store: Authorize or deauthorize your Mac or PC

Computer and iPod are however associated with an Apple ID

iTunes Store: Associating a device or computer to your Apple ID

Disassociating the iPod will not effect media currently on the iPOd. Y will not be able to redownload previous purchases