Dave, the electric field works because the wire diameter is small. This causes a very high local e-field which ionises some component of the air. Your professor may be right that it only works on dust particles, and not the air itself. So far only very light structures have been demonstrated...
If nitrogen could be ionised, there might be potential at supersonic speeds. The electric field would guide the ionised air to avoid the conventional shock wave, with consequent reduction in noise signature. I suspect the power requirements are prohibitive though. Besides a better approach is to build up the shock in smaller weaker shock waves, for example using a staggered pitot tube.
Still, good to think outside of the box...