Assuming the iPod keeps all the playlist information you need (I can't think of anything aside from maybe custom EQ settings it wouldn't have), yes you can upload the stuff from your iPod onto the new computer. You'll need third party (but usually free) software to do so. And I wouldn't remove the library on the first computer until you've confirmed everything is working on the new one.
But all you really need is the playlists, the play counts (I *think* the iPod stores and collects these), and all the song files with their already-inputted MP3 meta tags, right? There shouldn't be a problem with that...