The engine has a rough idle when the A/C is on?

Hello, it sounds like the A/C Compressor is failing. There are no more IAC valves on newer vehicles, everything is controlled by the PCM, so idle control is done by the PCM moving the throttle plates as needed. But this vehicle might have a variable displacement compressor, they have a swash plate that moves around to different valves inside the compressor to regulate pressure. If there is no compressor clutch on the front. If it is making that much noise and is affecting the idle of the vehicle, then it is putting too much load on the engine because it's probably seizing up. If it does eventually seize up completely it will break the belt and leave you stranded. So, I wouldn't use the ac or defrost until you get it fixed.
I don't see any technical bulletins on the ac compressor, so it will have to go in to be checked for correct operation.