Sorry J_J but I must disagree.
Closed center main hyd pumps are always turning when engine is running BUT not always pumping oil. When the hyd pressure builds up to the "set standby pressure" the stroke control valve causes pressure oil to enter the pump crank case which forces the 8 pistons(on larger pumps) away from rotating pump shaft which makes pumping cease. When pressure in crank case drops below stand-by pressure springs force pistons back against rotating shaft and pumping begins again.
If you have pressure at the IN port, you must have fluid flow, no matter how little.
If the CC pump is totally destroked, you have no flow, or it is attached to an accumulator, which might supply pressure.
Excerpts:
Constant pressure systems (CP-system), standard. Pump pressure always equals the pressure setting for the pump regulator. This setting must cover the maximum required load pressure. Pump delivers flow according to required sum of flow to the consumers. The CP-system generates large power losses if the machine works with large variations in load pressure and the average system pressure is much lower than the pressure setting for the pump regulator. CP is simple in design. Works like a pneumatic system. New hydraulic functions can easily be added and the system is quick in response.
Constant pressure systems (CP-system), unloaded. Same basic configuration as 'standard' CP-system but the pump is unloaded to a low stand-by pressure when all valves are in neutral position. Not so fast response as standard CP but pump lifetime is prolonged.
Load-sensing systems (LS-system) generates less power losses as the pump can reduce both flow and pressure to match the load requirements, but requires more tuning than the CP-system with respect to system stability. The LS-system also requires additional logical valves and compensator valves in the directional valves, thus it is technically more complex and more expensive than the CP-system. The LS-system system generates a constant power loss related to the regulating pressure drop for the pump regulator: