You may be correct. Here is a description of the AAR's function from the CIS primer:
"Provides extra starting air (bypassing air around the throttle body) with a cold engine. The valve slowly closes with heat, provided by an internal resistor, and to a lesser degree, from heat from the engine itself. For part number 0 280 140 200 (from a 1976), the cold resistance of the heater is about 17 ohms. This device was added in '76.
Failure mode: May remain partially open in cold ambient conditions due to open resistance element. Idle speed stays high after warm up. If it stays closed due to mechanical malfunction, the car may be hard to start."
CIS Primer for the Porsche 911
I put my AAR in the a 200 degree oven a month ago and it took 10-11 minutes to close. Maybe your 15 minutes from cold includes the extra few minutes to warm the engine exterior up.
Only thing I don't get is that if "all that is wrong" is an open circuit, the re-opening (after warm) should still take quite a while.