... This is all ignoring the fact that orbital mechanics just wouldn't work if there was air resistance. The planets would quickly slow down and crash into the sun.
But imagine this: a breathable nitrox atmosphere co-orbiting with the planets. Each planet is roughly at rest with respect to the local atmosphere, so no drag. Just lots and lots of wind shear. Probably planetary scale vortices. That'll sap orbital energy into heat, so probably not stable, but pilots can probably exploit it to acheive velocities comparable to orbital velocities over time. I think you'd probably have to have two sails connected by a tether, sufficiently far that their air streams are at significantly different speed, with one of them acting like a keel.