If you mean, do they cause all potholes, certainly not.
Potholes exist in many parts of the country which have no gophers.
Water damage causes most of them, I believe. If you mean, do they cause some potholes, I doubt it. Paved roads are built with substantial roadbeds, going down a foot or two, of crushed rock, which gophers don't seem likely to want to tunnel through. Argonne National Laboratory, Division of Educational Programs, Harold Myron, Ph.D., Division Director.