Yes and no. Correct on how recip compressors work, but screw compressors will still shut off/go into a standby mode if there is no demand. Almost all screw compressors will have an idle timer of some sort, they will run on idle before eventually shutting down and going into standby. See below the next quote for what happens when the compressor is up to pressure.
Correct Shawn. The inlet valve that allows air in to be compressed is closed during the idle period so it’s not pulling in volume to compress. The lobes of the rotors are literally just sitting there spinning but not doing anything. Then when the pressure switch calls for it to load, a solenoid closes off the blow down line and commands the inlet valve to open, completing the circuit and allowing air to be compressed.