Good post from jgll. I'll add one thing.
I'm not certain the a/c compressor clutch will engage
without the engine running. It likely depends on the
particular model/year of the car.
My 1987 124 uses the dreaded Klima relay to control
compressor clutch engagement. One of the functions of the
Klima relay - at least on diesel models like my car - is
to deactivate the compressor when engine RPM falls below
a certain level. In my car, the compressor won't engage
unless the engine is running at 600RPM.
Early Klima relays waited for 10 seconds after the engine
reached 600RPM to engage the compressor. This was really
annoying down here in Texas. The newer Klima relay I now
have installed seems more aggressive in engaging the
compressor, but I'm still certain it waits until the
engine is running.
As they say, YMMV.