Hi Jonathan, Mark,
Considering the way that the RaQ4i's are set up, I don't believe it's a possibility. But, i'd love it for someone to prove me wrong.
I can't prove it, but I *think* it should be possible. I don't have a spare RaQ laying around either.
My suggestion would be to build it all through either source or srpms. Since the RaQs are lacking a video card (as they should, imho), you'd need something in the line of VNC to connect to your newly created desktop. You might need some additional software like maybe png, jpeg and whatever libraries, but this could pretty easily be installed from srpm from the Rawhide 'distro'.
I know there are people who have succesfully installed XFree86 on Trustix (http://www.trustix.net), which is a server distribution *only*. Hence, no X.
The latest XFree86 srpm is somewhat over 50 megs, so I think you'll need patience and lots of coffee...
Good luck... Nico