Mirrors usually flip back when not energized so that debris from mounting a new lens does not reach the sensor. They are also hold in place in some mechanical means, so when not energized, they do not shake and vibrate during transportation.
Mirrors with only one latching position (e.g. spring pulls it to a closed position) will require power to keep the mirror up against the spring.
Mirrors that have two latching positions (can lock in both up and down) will not use energy when latched but will use double the energy when moving the mirror in a shot (because the camera has to overcome the latching force two times). A sudden power down will leave such a camera with either mirror up or down.
Mirror up on Nikons do use power, as a surprise power down will show that the mirror is snapped down.