I did some more sciency research.
"Food travels down the oesophagus at a rate of approximately 3 to 4 centimetres per second (1 to 2 inches),"
Okay, a good-sized hot dog is about... maybe 8 inches long, and about 1.5 inches wide
"“The normal esophageal diameter should be two to three centimeters, so they can have quite a stricture before theyfre symptomatic.â€
The only reason why deep-throating is possible is because you relax your throat. When you're choking, you're panicing and your throat is going to tighten up.
Now, we say 1-2 inches per second, down your esophagus that takes 7 seconds to pass down a single, normal-sized, chewed up piece of food
That's going to be about 8 seconds with an object that is too large for your esophagus to handle
You're going to choke
EDIT: Actually that will be about 15 seconds it takes to get down your throat, accounting for the remainder of the hotdog.