Once depleted, the unit will still be operable, but the movement is heavily restricted as it is dead weight.
For power armor to function it requires a fusion core as a source of power, which drains over time actions that consume AP will increase the rate of depletion. Power armor is a multi-component armor unit, comprised of a base frame, with assorted armor pieces mounted on it.
Power armor is a unique form of external armor in Fallout 4.