It is my understanding that the tank does a 'dump' and re-pressurizes each time the vehicle is started.
That said, I just replaced both of my rear, self-leveling air shocks on my '15 Tahoe due to leaks. A couple of times I would exit the truck while it was running and the damn compressor was running - got worse-and-worse. 94k mi.
From:
https://www.underhoodservice.com/servicing-gm-autoride-rear-air-suspension/
Each time the compressor is activated, the ESCM commands ON the exhaust valve for 1.5 seconds to release air from the compression chamber in the compressor’s cylinder head ensuring low motor current draw upon compressor activation. The ESCM also limits the amount of compressor run time to 255 seconds to protect the compressor components from thermal damage.
The system also performs a self test on each ignition ON cycle in which the ESCM commands the ELC relay ON, activating the compressor for 4 seconds then monitors the position sensor’s signal voltage inputs to verify the compressor is functioning and the system is holding air pressure.