https://www.sciencedaily.com/releases/2013/08/130808123719.htm
Nope, not based upon how scientists define "feel" and "pain."
https://www.ncbi.nlm.nih.gov/books/NBK99533/
It's doubtful that they even feel "pain" as information, since pain is defined as including an emotional event. E.g., people don't feel pain while under anesthetics.
I've been under many times, and did not feel any pain; although I have all the functions needed to feel it. Otoh, when I tore my achilles, I was under emotional distress, although physically at the time it snapped and at every point afterwards, I had no sensation of any pain whatsoever. Then, there's emotional pain.
People who are paralyzed often have to be put under anesthesia because while they don't "feel" anything in the way the rest of us might describe it, their body does in fact know there is something going on, and it reacts (sometimes dangerously) during operations and procedures.
Simply having reflexive or instinctive responses to stimuli, no matter how significant the amount isn't pain.