Nothing I know of is 100% efficient, except for my Mom at remembering to mail out birthday cards on time; no, reactors are not 100% efficent. I 'think' in a real plant something like 15-20% of the energy/heat produced by the reactor actually is used to do work in the form of propelling a ship and/or producing electricity.
If the laws of thermodynamics "took a day off" I would create my own castle with 70 virgins and a built in Taco Bell from empty space because energy would no longer be conserved, cold would 'flow' to hot, I would break every piece of glass I could find to watch it spontaneously put itself back together, and then I would fly to the moon on a pink elephant that I gave birth to from the same nothingness as my awesome new bachelor pad!
My point is this, if thermodynamics "took a day off", I believe anything would become possible, which would probably include your 100% efficient nuclear plant! ;) You can consider c^2 as nothing more than a 'conversion factor' which equates a little bit of mass (m) to a lot of energy (E) capable of doing work. I too think it amazing at how much energy can be extracted from a well designed 'hot rock' (aka 'reactor'). Thank you Dr. Einstein for realizing that (1/2)*m*v^2 = (1/2)*(E/c^2)*v^2!