Can ArcPy test for availability of SDE Connection before trying to use it?

Yes, you can do something like:

try:     
      if arcpy.Exists(PropertyTax_Parcels):
         arcpy.AddMessage("Checking core Layer found? Yes and online")
except:
      raise Exception("Layer not found")

You just define it as a static layer in your SDE and if so it can continue; other wise you else out of the script. I do this in many places and will actually log and fire SMTP messages if my connections are lost in core apps.