Yes, I'm afraid so. Make a block diagram of the Refrigerator with the mechanical power input, the heat input from the refrigerated space and the heat rejected to the condenser.
Input the heat rejected to the condenser as the input to a Stirling engine, and the heat rejected by the Stirling to atmosphere to see what the power out put of the Stirling would be.
Much less than the power required to run the refrigerator.
Second Law and all that! Then that devil entropy