You can backup and/or transfer iThingie goodies to another computer, but this only includes stuff you purchased from the Apple Store. Nothing you side-loaded via iTunes will get backed up, at least in my experience. Therefore if you try to Sync you will probably lose all of your side-loaded stuff! I haven't tried and tested this, nor will I. But that is what it appears to do. So beware and be cautious! iTunes can turn wicked on you in a heartbeat and if you don't fully read and correctly interpret its popup caution messages you can wipe out a lot of stuff.

I base the above statements on having just installed iTunes on another computer after my primary computer died. I went through the Transfer Purchases from iPod to the new computer option, then did a backup, but only purchased items transferred. If I ever restore from this backup I will lose side-loaded items.