Choke pull off and Fast Idle? Related?

No.

When you get into the car, and don't touch anything, the carb should be on the NORMAL "curb idle" screw

The properly adjusted choke thermostat is putting spring pressure against the choke linkage

When you floor the throttle, this moves the throttle away from the fast idle cam and allows free movement. The spring tension of the choke thermostat then "sets" the choke butterfly CLOSED as well as "springs" the fast idle cam into place.

When you release your foot, the throttle then stops down with the fast idle screw stopping on the fast idle cam. Again, the choke at this point is normally ALL the way shut.

When the engine fires, the engine would choke itself to death if the pull off was not there. The manifold vacuum seats the pulloff, which opens the choke butterfly a small (specified, adjustable) amount. This then opens the choke butterfly enough that the engine will run without excessive choking,

and of course, as the choke thermostat warms, it slowly opens the choke more and more, as well as dropping down the fast idle cam. The choke normally opens, and the fast idle cam drops due to gravity.

The pulloff does not affect this because it uses a slot somewhere in the linkage. You must realize, that the pulloff OPENS the choke a tiny bit from CLOSED, but because of the slotted linkage, does NOT RESTRICT further opening.

You can see this happening yourself.

With the engine stone cold, remove the filter so you can see. Carefully watch the linkage, the fast idle cam and ONE time open the throttle wide and let it go back. You will now see that the choke is closed, and the fast idle set.

Start the engine, and you will notice the pulloff pull in, and the butterfly pull open a small amount.

To simulate the choke warming, you can gently pull down on the thermostat link, and bump the throttle just a tiny bit. The fast idle cam should fall down as you hold the link down a little, and bump the throttle.