I just did a minimal test in Blender 2.79:
- I set up an armature of 3 bones
- I recorded some 100 frames of skeleton data from NI mate 2.14 with Kinect 2
- After recording, I added a constraint to 3 of the bones to follow the left hand bones
- I duplicated the armature, selected the duplicated armature
- Bake Action -> frame range -> remove constraints
- The duplicate armature still has constraints
It either seems like the way animation baking works has changed, or there's a bug in Blender with this feature.
You can still export the rig as BVH though, even if it has the constraints included in it.