Sure, it would work. Where are you going to get the "unlimited power"? Not even nuclear power is unlimited. It could be used to produce heat, which would be used to kick something out of the rear of the spaceship.

You just need something 50 times the mass of the payload (including that nuclear heater). So 1 part living system & heater, and 50 parts reaction mass to kick out. Now, how heavy is a nuclear reactor that can heat water (or whatever you're using) to super hot plasma?