If you did, you'd exite it once and it would then be shot into space.

Instead, you'd entangle and excite to white heat a platinum plate in the nozzle of the caesium engine. This would transfer energy to the caesium fuel and expell ions into space as a continuous stream until the tank ran dry.

And my understanding of the energy conservation aspects are that "cold" would effectively be teleported back to the plate's counterpart on Earth whilst "heat" would be teleported outwards. Thus, energy is conserved.

Might do some funny things to thermodynamics, though. Quantum entanglement apparently offers a way to transmit energy equally efficiently, regardless of the temperature difference...