Could go either direction, depending on the prop design. I once found a good description of the McCauley prop and control and was impressed with the astuteness of its balance of forces and torques in the prop hub.
EDIT: per
http://www.mccauley.textron.com/von_..._propeller.pdf, in the McCauley prop, oil pressure decreases blade pitch - like the following models.
But among other prop designs, a counterweight type will probably slew to the high pitch (aka coarse pitch, low rpm) stops. This is by design intent, to prevent overspeed in case of loss of control oil pressure. Older H-S and Hartzells as well as Dowty are this way. Thus, for takeoff/climb, oil pressure is used to drive blades to low pitch.