GNUstep barely focuses on Cocoa compatibility, but it seems like it's
almost ignored to them. If you have applications for Mac OS X that
don't rely on Cocoa or any other proprietary part of Mac OS X, you can
use it on Darwin (provided you have source code).
You won't need an entire operating system, as Apple already provides
it freely (as in freedom). You'll just need to clone the graphics
systems (well, there's many other proprietary components, but the
point is that you already have a free OS to built on, Darwin).