Actually, no it wouldn't. The only way you're going to get no spanwise flow is from a 2D wing (a.k.a an infinite wing, or some approximation thereof). The only drag that a 2D wing suffers from is parasite drag.

A 2D wing, has no induced drag because it has no induced downwash. In a 2D wing, upwash always equals downwash... this is not the case in a 3D wing. In a 3D wing, energy is lost (from lift) to the trailing vortex sheet. This vortex sheet induces downwash.

The tip vortex is simply the "rolled-up" vortex sheet caused by a 3D wing moving through a fluid. You CANNOT prevent the tip vortex, but you can modify it. Modifying it by effectively spreading it out further from the other tip (which is what a cutoff, Hoerner, or end-plate does) can reduce drag.