Are OS X and PureDarwin binary-compatible
Yes - as long as you do not rely on a library or other feature that is only available in OS X.

The Pure Darwin project is a continuation of the Open Darwin project which was founded by Apple and a non-profit organization called the Internet Systems Consortium. This effort came to an end on 25 July 2006. Pure Darwin continues where this left off and promises a lot more than just binary compatibility with X11 available in the current developer preview (released in 2009).

The site says they're looking for people to join the project...