Once the vines reach the trellis, they will climb straight up, regardless of where they were positioned in relation to the trellis. It may take some training to get them started, and some varieties are better climbers than others.

My cuke trellis (which was an earlier pea trellis) is in a N-S orientation. Works well to evenly distribute the solar hours from one side of the trellis to the other as the sun rises and sets. Powdery mildew seems less and later compared to my ground crawling cukes. As for training the vines it's a weave as you go job and ties can help for the more stubborn vines. They'd still be just as stubborn at going E-W is my guess.

As others noted, orientation is not as important as getting the climbing process started. I first stick a cage over cuc hills and them support plastic mesh above that. Only occasionally do I need to position a branch so that it will climb the mesh.