No. Not at all. With an educated rider, the bit will cause zero pain. It is not used to first cause pain, and then the horse obeys out of fear, curls, or backs off the contact. That is not how these bits are designed to work. That is not how educated riding works.
Now, an uneducated rider who who has no understanding of how the horse is ridden off of the seat and how to carefully manipulate these bits will cause pain because they will use the bit in the WRONG WAY. These bits move in millimeters, maybe fractions of millimeters. Imperceptible to most of us.