I am not assuming that you had followed the advice that was given to you. If anything, it is bad advice given the function that the crankcase heater is there to perform.
In colder climates, the crankcase heater is a required component of the air conditioning system. Because of the cooler temperatures, the outdoor AC unit is not going to be running for months at a time. During this time, if the crankcase heater is not powered on and able to prevent refrigerant from sitting in the compressor crankcase. The oil that is in the refrigerant will break down and dissolve.
When the compressor starts up again the next spring or summer, the oil has lost a considerable amount of its viscosity. Thus effectively shortening the life of the compressor.
Will turning off power to the outdoor AC unit save money? No, not any amount that you will see on your bill. Will it damage the condensing unit? Yes, in the long term it will cause unnecessary wear and tear and it will cost you more in the long run.