I read what you wrote again and now I think I understand what you are trying to say. Let me try to explain it another way and let me know if it is the same...

​​​​​In motorcycle class, you are taught that if you want to turn right, you push the right handlebar forward. That's counter steering, which precipitates a shift of the tire's contact patch from the centerline of the tire towards the edge and the familiar lean. In a way, it's kind of a controlled fall to the right counteracted by the forward momentum of the motorcycle. That's precession.

The same thing happens on a bicycle. When you push the right bar forward (you may not think of steering in those terms but that is what is happening) the bicycle begins to lean, countersteer, and precess. The force required to initiate the turn and the sensitivity and stability whilst turning depends upon a number of things, including rake, trail, tire circumference, etc...

Now imagine riding no hands and the bike starts to lean to the right. Without touching the handlebar (imagine flat bars for easier visualization), the right handlebar has pivoted forward (with the steering axis as the point of rotation). Since the head tube is not vertical but rather raked, the tip of the right handlebar is now vertically higher than the neutral position. Not a lot - millimeters perhaps - but is is higher. And the because of gravity, the tip of the right handlebar wants to return to it's lower position thanks to gravity, so it exerts a "corrective" force that helps bring the bike back to vertical.

To make this idea clearer, imagine a really relaxed head tube angle - say 45 degrees - and a comically long stem - say 1 foot. As the bike starts leaning and falling to the right, the tip of the right handlebar will rise considerably and gravity will pull it back towards center. Now imagine the same head tube ange but a 0 extension stem; the tip of the bar will rise but not nearly as high.

(to model it more precisely, you really need to be looking at the center of gravity of the handlebar plus stem and how that CoG relates to the steering axis. The CoG is likely near the juncture of the stem and bar, and it rises if the bike falls to the right.)

This kind of makes sense. A longer stem will push the CoG further away from the steering axis thus creating a greater "corrective" moment force upon that axis. Imagine, for example, 2 lb weights at the end of the handlebars. A longer stem will exert a stronger "corrective" moment upon the steering axis vs a smaller or 0 extension stem.

With all of this said, whether a bike with 0 stem extension can be ridden no hands or not likely depends upon front end geometry and tire profile as much as anything. Also note that a rearward facing stem will exhibit the same behavior as a forward facing stem in this no hands example.

Is this what you were suggesting?