No, when your power plant reaches 0%, its output drops to 40% and then stabilises at 50% a bit later. Any further damage your powerplant takes can lead to a spontaneous explosion - higher damage like rails have a higher chance for that.
You usually can (and should) set your power priorities in a way that you are still able to escape at 40% power (thrusters, FSD plus sensors; defensive measures like point defense, chaff and heatsinks if possible, anything else like life support is a bonus). Depending on your setup you might even be able to power some weapons.
NPCs use a similar approach, but since they have more power, are fast at disabling/enabling modules, and it can be hard to tell if they fire all their guns or only half, the easiest way to see is them not recharging shields.