I think the question concerns fixed pitch propellors, as such talking about feathering, of coarsening of the prop is simply not relevant.
If the fixed pitch prop is stationary, it is presenting something close to a 90° angle of attack to the airflow, and quite a bit of drag is associated with that.
As the prop rotates faster and faster, the angle of atack reduces, and so does the subsequent drag.
If the engine is producing any power at all, the prop may rotate fast enough for a 0° AOA - this is the "zero thrust" that is set for twin engine practice to simulate feathering.
Increase the power past this point, and the prop's AOA goes from negative to positive, and the prop begins to produce thrust.
The argument about the airflow providing the energy to rotate the prop is correct (where else would the energy come from), but it is incorrect to state that a stationary prop is not extracting any energy from the stream, it is just wasting this energy in form drag.