My 2002 denali idle's poorly when the air is turned on.

Pull air intake hose off of throttle body. check to see if throttle plate is gummed up with black/oily residue. if so clean the throttle body with air intake cleaner and toothbrush. if the throttle looks clean, then the iac motor is sluuggish.if it has a throttle cable you can replace just the IAC motor. if it doesn't have a throttle cable, the IAC is part of the electronic throttle control actuator and has to be replaced as a single part.

When you turn on your a/c the engine should idle higher if not solinoid not working or wire broken,or vacume hose leaking it will be near the throtel ontop of engine