Yes. Having high arches suggests that the foot may not flatten (pronate) as much as normal when you walk. This means the foot is more rigid. A rigid foot puts extra pressure on nearby joints and soft tissues.
The main joint of the big toe doesn’t move as much in people with high arches. This puts an extra strain on the toe. It can also put added stress on two small bones under the main joint of the big toe. These bones are called the sesamoids.
So high arches can lead to arthritis in the big toe joint. And arthritis in the big toe joint can in turn cause arthritis where the sesamoids join the big toe.