It's a very interesting idea. It would make a unique sort of Linux distribution!
Actually, a project like this has been attempted before: to build a BeOS compatible system on top of Linux. It was called BlueEyed OS, originally just BlueOS. I believe it didn't get very far. :¬( Haiku is the whole thing from the ground up - clean reimplementation, like ReactOS is for Windows - and it's doing much better.
Less of a new OS, more of a sort of turbo-emulator, was Amithlon. It's dead now for legal reasons but essentially it was a small custom Linux distro that booted a PC straight into a Just-In-Time compiling Amiga emulator and thence straight into an Amiga desktop. Essentially it was a boot CD that turned a PC into a fast Amiga. Very nice if you like that sort of thing!
(This is based on a post from the ROX mailing list; I just thought it might be interesting here.)