A helicopter in a stable hover is producing the right amount of power (lift) to overcome the weight of the helicopter. The engine and blades are doing work because gravity wants to accelerate the aircraft down. Gravity is a constant, so there is always a downwards force, so therefore even if the helicopter is in a stable hover, (vertical - upwards) force is still being applied.
To raise the collective to increase pitch to provide the induced flow and therefore create lift also increases drag on the blades and the blades want to slow down. Engine RPM must be increased to maintain a stable engine RPM and therefore a stable rotor RPM. So as the aircraft lifts, the engine produces more power. In a Robinson R44 for example, the manifold pressure would be below 18 inches at idle and then increase to about 20-21 inches in the hover, but MCP (Max Cont Pwr) might still be about 23.4 inches to allow transition from the hover to forward flight.
Does that add anything to the helicopter theory above?