Yes, pole climbing is one of the many skills taught as part of "typical" lineman training. Depending on the task and environment, they might also use a lift (bucket truck) to access pole-mounted cable and infrastructure. Being able to perform the work in a safe manner is definitely the primary consideration. Although lifts are a great tool for the lineman, there are situations where it may be very difficult to access using a truck. In those cases, the lineman may be required to climb a pole. Here's a good video introduction to pole climbing: https://www.youtube.com/watch?v=3yFId43B0c8
I'd also recommend researching apprenticeships and training through the International Brotherhood of Electrical Workers (IBEW). The IBEW is one the primary collective bargaining organizations (union) representing skilled workers in the utility power industry.
I wish you the best success in your career and educational pursuits!