I have spent approx $1300 having the AC compressor replaced on 2002 Mercedes-Benz C240

The car signaled that the engine needed to be shut down and had a thermo on the display in the red initially. Since the compressor has been installed, the shop state they were unable to get the pressures to read right. Can the car be driven without damaging the engine? Was it really necessary to get the compressor installed or would it have affected the engine?

Asked by for the 2002 Mercedes-Benz C240