Power is needed to overcome the drag of the blades to provide the lift you need. Higher RPM means slightly less angle of attack is needed to produce the same lift than a lower RPM, so the drag will be slightly less than trying to produce the same lift at the lower RPM, and you will magically rise into the air..
Of course, that is correct but, with respect, I would argue that the fundamental gain in the practical scenario described -of trying to get off a deck at high AUM - is down to the increased torque margin available, and the greater power going into the rotor once the MGB torque limits are reached.