Is it theoretically possible for DirectX to work on OS X natively?
It's more than theoretically possible, it's how many PC games are ported to run on OS X - using Cider from TransGaming.  This is from TransGaming's web site:


  Cider works by directly loading a Windows program into memory on an
  Intel Mac system and linking it to an optimized version of the Win32
  APIs. TransGaming's Cider implements common multimedia Windows APIs
  such as Direct3D, DirectInput, DirectSound and many others by mapping
  them to Mac equivalents.