Moved to iPhone Jailbreak.
You can sync a jailbroken iPhone with iTunes with no problems. Not backing up is risky because you'll lose a lot if the phone crashes or is lost. The iTunes backup could be used on a replacement phone or after restoring. A common misconception is that it will automatically update the firmware. It asks you if you want to update and you have the option of declining. I recommend updating as long as your phone isn't unlocked. If it is unlocked, you'll need more specific instructions to retain unlockability when updating.
You'll have to rejailbreak after you update, but you can backup your jailbroken apps with PkgBackup. You don't need to restore. Just hit the update button after syncing and backing up. All your apps, settings, data, bookmarks, contacts and media will still be there. It will update the 3G to 4.2.1 and then you can rejailbreak with limera1n or greenpois0n.