If you put a hungry pigeon in a Skinner's box with a food dispenser that gives food by timer, every few minutes for example, the pigeon will soon make some kind of rituals to get the food. Like, turn three times left and peck the corner of the box, or move head up and down, or flap the wings and make sound.
In fact, he gets the food randomly or by timer, so it doesn't matter how he moves and what he does.
I mean no offence, but your hypothesis is ridiculous.