Exported mesh is built against reference pose of armature and mesh objects, not that you see in blender.

In qc there might be $definebone lines that re-define reference pose.

No, they won;t be kept for model, but you can make animations, and all constrainted bones motions will be re recorded and exported as well.

I did never import .qc file as it was always buggy and did import many unnecessary information.

Does the model exist actually?

There wan an error during compile. Put compile log here.

Vertex Groups are just kept. There is a trick, you can just change armature of model to Valve's one and re-name respective vertex groups to Valve's armature bones, though the result might be not so perfect.

in blender, enable Weight Link Cull Threshold. Re-export model.

Yeah, looks like smd error. Thanks for pointing.

I cannot import this particular smd into Blender.

Blender version: 2.79b
BleST version: 2.10.1

smd: https://drive.google.com/open?id=1pOj7C4DohOyT6OnSl7t9rgmYxz4E73Y5
traceback: https://postimg.org/image/aro863wdx/

Hmm, I'll try batch replace shape object in all bones with simple script then. Thanks for advice.