Car seizing when A/C or heater is on

Last week my car made a grinding sound upon starting. Thought it was starter took it to mechanic they did not hear anything but replaced the starter anyway. Driving on way home I turn on blower/ac car was making a noise and seemed the car was moving slow. Turned off the ac took it back to shop. They then tell me my ac compressor is shot and that it would not cause problems. This morning I turn on heater to defog windows my whole engine seized and was smoking. Can the a/c compressor cause this issue