Can I update my iPod from more than one computer?
In the official company FAQ, Apple reports that:
Yes. When you first connect iPod to your computer, iPod recognizes that computer as its "home" computer. Each time you connect, iPod automatically downloads the music library stored on it. When you connect iPod to a different computer, iTunes will inform you that iPod is linked to a different iTunes library and will ask whether you wish to erase iPod's contents and sync with the new computer's library.
If you will be connecting to multiple computers frequently, configure your iPod to manually manage music. This will allow you to selectively drag songs, albums, or playlists from the second computer to your iPod without compromising the existing music.
For additional information regarding using your iPod with more than one computer, please refer
to "Using iPod with Multiple Computers" from the Apple Support Site.