I performed such a study to diagnose stomach problems twice with different specialists. There was no pain as such, but the gag reflex does exist. It can be suppressed with the help of anesthesia and with the help of ... believe it or not, by willpower. When you know that the examination is necessary and the probe should be tolerated, then the discomfort decreases enough to transfer the procedure without any problems.
I would not say that this procedure is painful, but I can definitely say that it is not very pleasant. The gag reflex does not disappear anywhere, and the feeling and the realization that something has been shoved into you and is climbing inside is disgusting.
I swallowed at one time, as a child. There is no pain, before the procedure, a special solution is sprayed into the throat. But it's not very pleasant, it's hard to breathe. I didn't really succeed to carry out the procedure to the end, I started to twitch.
Zones D or zones T , I certainly did not try, but assuming that when swallowing, such objects will tear flesh and excite nerve endings , my answer is yes!
But there are heroes who can do it effortlessly:
Jake from Adventure Time
Specialists from NASA