I haven’t tested this at all because I don’t have an iPod shuffle, but in theory this should work.
Install this little tool that makes your gmail account look like a drive. Tell iTunes to use that drive to store its music. Sync up your iPod Shuffle, and know that gmail is keeping a copy of everything on your Shuffle.
The transfer rates between iTunes and gmail probably kill this idea, but it’s fun to think of anyhow. Also damning the idea is the fact that most people have libraries larger than 1GB, and if your computer loses its brains (making a backup useful) the only way to get at your files is to download them one by one, or install the drive extension tool above on another computer.