rubik101, we miht have crossed wires at the moment.
Before running the hydraulic pumps the reservoir has to be pressurized. However this does not mean that the APU has to be running and the bleed system to be pressurized.
During maintenance we have to release pressure from the hydraulic reservoir by means of an depressurization valve. This will remove all pressure from the reservoir. After this has been done you need either bleed air to provide pressurization or an external air supply. Runnig the pumps without the tank pressurized increases the risks of cavitation.
In normal day to day operation of the aircraft the pressure on the hydraulic system should be maintained be a check valve in the pressurization module.
So for a pilot, as long as the tanks have not been depressurized by maintenance you can run the pumps on the ground without the APU or the bleed system pressurized. However may the system have been depressurized by maintenance or a faulty check valve then the system needs to be pressurized before runnig the pumps.
Leaving the hydraulic pumps running on the ground (when not required) is bad practice and puts people in danger. Yes, I agree you will be able to see a leak quicker. However, several times in my career we had such a small leak which was only evident by a fine mist in the wheelwell (and declining quantity indication in the flight deck). So the poor bugger going into the wheelwell has the hydraulic fluid all over them. Not a good practice and something which should be avoided.