What is the history of this car? How long have you owned it? Did this happen after a recent repair?

The AC does not pull enough mechanical engine power to drag the motor down as you describe so you are going to have other issues.

This car uses drive by wire, there isn't a mechanical cable that runs to the throttle body, the gas pedal sends signals to the engine computer. Mercedes tends to place a bunch of ground wires under one bolt. If the bottom and top ones corrode, the middle ones start to communicate with each other and all sorts of odd behavior can occur.