Mono on non-Windows platforms ships with a static library called io-layer that implements a small subset of the Windows API for compatibility reasons, without any server processes or a registry. It does not (normally) attempt to do any path translation, so I think that's as close as possible to what you want to achieve for those low-level api's.
Of course, there's a limit to the level of compatibility (even if you're only looking for source compatibility) you can achieve without the sort of architecture Wine has to simulate services that are available on a real Windows system. Combine this with the fact that the Windows API just isn't very nice to program against, and it leads to little interest in a project like this.
But maybe it would be possible for one person to pull this off for a large enough win32 subset to run a GUI application, using the code already available in Mono and Wine.