Either way you can use power aor with a depleted fusion core.
If your fusion core gets depleted you cannot use VATS, you cannot use power attacks, and you move slower.
However you still have are walking tank, even if you are a slower walking tank.
can you eject from the dead unpowered armor mid combat? say a death claw grabs you like in the video is going to finish you off . can I eject from the armor save myself and then fight with just regular armor from my inventory and my hand weapons?