Would an electric fence be able to detect being bypassed?
The only way a detection could be feasible is looking for changes in signal reflection. Neither resistance nor inductance will provide reliable information of bypassing activities, especially not with a mile long fence wire. However, with a sharp peaking signal (already present due to the nature of the electric fence) and analysis of the electrical reflection pattern might provide an usable information to detect bypassing. The term you want to look for is Time Domain Reflectometry. See: https://en.wikipedia.org/wiki/Time-domain_reflectometry