Yes, but the accelartor pump is pumping air then....
You stated that "crank it witout touching the pedal first" was the key which is incorrect.
The bowls will fill with the choke set or open when rotating the engine and running the fuel pump.
Filling the bowls is separate from the choke position which just reduces the intake of air causing the engine to draw more fuel versus air.
You can set the choke and then crank it to fill the bowls and finally pump the pedal to activate the accelerator pump.
I know its a minor point but I thought it was worth pointing out.
This is the inherent problem with carburetors they aren't always perfect when the temperature changes.
In general you would like to stay on the
lean side to get the car started. Just enough to get it to fire.
Too many accelerator pump shots and you're dumping raw fuel into the cylinders and washing the oil off the cylinder walls.
This means
WEAR.
Back in the 70's and early 80's it was common for many everyday car engines to start burning oil, lose compression and power due to worn points, sticky or misadjusted chokes etc...
In the northeast the small block LA engines had a bad way of developing ice in the venturi and getting
really rich after 5 minutes of running on damp 30-40 degree weather.
But I digress...