Absolutely incorrect,
barit1.
Repeating my post above:
Prop governors sense prop RPM, and adjust the pitch to compensate. If the RPM drops, the governor commands a finer pitch - if the engine is running, this reduces prop angle of attack, and thus prop drag and the RPM increases back to the governed level. If the engine is not running, the RPM drops, the governor commands finer pitch, this increases angle of attack (relative wind is striking the front face of the prop in a windmilling situation) and the relative wind thus drives the prop faster.
Finer pitch when the engine is producing power increases RPM.
Finer pitch when the prop is windmilling
also increases RPM.
In the first case the engine is driving the prop, the airflow is striking the prop on the "back" of the blade (the side the pilot sees) so a finer pitch reduces the blade angle of attack, decreasing the drag and so allowing the engine to spin faster.
in the second case
the airflow is striking the prop on the "front" of the blade, so a finer pitch
increases the angle of attack from the relative wind, which
increases the force that wind is applying to spin the prop, which increases the RPM.
The prop governor thus controls the pitch in the correct sense in both cases.