The AAR works off a similar design as the WUR, using heat to bend a spring. As long as you have heat you have bend, so yes the AAR will continue to close with engine heat as well as electric heat, same as the WUR. That is what keeps the idle (AAR) and control pressure (WUR) correct at warm start-up. There is diminishing return as the bimetallic spring reaches its limit of motion.
If you are not going to adjust the AAR to compensate for missing smog equipment it can simply be removed and replaced by splicing in a vacuum line to the same thermol time switch that is used by the ignition distributor. Automatic function, no fiddling. If you do not have this TTS then use a solenoid. That huge CIS phalic symbol goes away.

Thinking of pulling my AAR of and giving it a slight tweak. Cold start idles at around 900 and surges just a little bit, i.e., a tad rich (control pressures are all in line) and I have the mixture set to lean best idle when warm. A little more AAR air would raise the rpm and settle down the rich surging I figure.
As for the TTS switch to the dizzy...mine is there but I doubt it's working; cannot get any voltage readings off the plug but works when bench tested.That will just lead to another topic altogether re: timing.