Ok, maybe "choke" is the wrong word. How about "gagging reflex". There can be so much wrapped around the bit that the horse starts gaping their mouth to rid themselves of all the balled up hay, but they can't because it is wrapped around the mouthpiece. I don't see how that helps them learn to hold the bit. However, generally, I have the young horse learn to wear the bit in the stall after eating a little (so they are more "satisfied"), and then I will "hang around" the stall/barn while he is in there wearing it (maybe clean other stalls, brush down cobwebs, etc.) I don't hover over the stall though, as I want the horse to figure out how to hold the bit on his own without me staring at him. I try to use an o-ring bit if I can, that doesn't have parts hanging down, like a half-cheek driving bit that he can get caught on the bars of the stall, etc.
I don't know of anyone around here that advocates allowing horses to eat while the bit is in. Actually, all the references that I found suggest that the bit be put in, and then the horse be worked on the longe line attached to the halter and not stay in the stall at all with the bit. In my barn, if the horse won't hold the bit within a half an hour or so in the stall for at least a couple of nights, I will go ahead and work them on the longe line even though they are still mouthing the bit. It seems to distract them enough that they learn that holding the bit is more comfortable on the jaw, instead of the feeling like chewing gum too much.
Myrna