Running with the Apple Watch 3 non-cellular. Can I leave my phone behind?
Can I use the non-cellular version of the watch for tracking my runs
  while leaving my phone at home?


Yes.  The Apple Watch Series 2 doesn't need to be paired to an iPhone to utilize GPS tracking because it's built in.

From a MacWorld article on the AWS2 and the GPS functionality:


  ...loved how the Series 2 and iPhone intelligently passed off route
  tracking duties. “Apple Watch just seems to know when it’s out of
  communication distance from its paired iPhone, and it gets a GPS
  signal without you telling it to. And if I do have my phone with me,
  the Workout app will let the iPhone do the GPS because it’s the
  bigger-batteried device.”


And from Runners World on the GPS functionality and the accuracy:


  The biggest update for the Apple Watch 2 is a new focus on fitness and
  the integration of GPS into the watch itself. The first version
  off-loaded that work to your phone, but not all runners like to carry
  a phone when working out. Now they don’t have to. In our testing,
  we’ve found the GPS accuracy to be on par with our sport-specific
  watches