Do a turboprop’s compressor and turbine rotors windmill when the engine is shut down and feathered?
A feathered propeller is designed not to windmill in flight, however in the case of a power turbine or even a propeller connected to both the compressor and turbine, it's far easier to turn than an old radial when in the feathered position. 

Nothing physically stops the propeller from turning when feathered beyond the force required to turn the power turbine/gearing or whatever the propeller is connected to and the air hitting it at the right angle. Straight airflow shouldn't turn it, however any flow from the sides would turn a feathered turboprop. Unlike a turbofan, the propeller changes pitch so the air affects it differently.