We've seen Captains Shunpoing while the walls are down (See all instances of Ichigo Vs. Byakuya). So no, it does not interfere with Shunpo. It only prevents airwalking and doubles as a physical barrier so that no-one can just walk into Seireitei.

Mechanics of Shunpo haven't really been elaborated, but it's really just leaping around really fast. You only need ground to be able to do that.

Airwalking, on the other hand, needs loose particles from air, and the walls work like magnetic lodestones, absorbing loose particles.