well for one thing you never said what country your car is.
i have the full fsm.
and linked it
tell you service manager (at GM) where in the schematic below
that can happen, show me.? ( i know these guy mix cars in their heads and he dont fix cars, he points fingers? right?
there is no HEAD pressure any thing. sorry !( there is a TOO-low and TOO high freon pressure ) but this is
to save the compressor for destruction. and is closed full time all the time.
pin 6 controls the fan (see it?)
if the over heat switch goes bad(opens or falls off) the fan slams on. to cool engine.
if the evap ices up the fan is cut to help de-ice. RTM.
if the motor ecu signals , over load (passing or pulling grades)
the ecu tells amp to cut fan and A/C.
if the ecu sees cranking it cuts all A/c
some AMPS have a thermometer in inside for ambient temps (mine does !)
of the ambient temps go to too low , the AC is defeated
the car will run to -40f but never the AC
on mine,the ambient when over (undocumented degree's (guess at 90-100 ) the front fan comes on with A/C (mine does)
that is OTTOH.