Your case B is the correct one. And yes, there's lots of evidence. As in: Every single experiment ever done on an entangled state. An entangled state, in its simplest form, is two particles describable by one wave function, not a sum of the wave functions of two independent particles.
If an entangled state as you describe it involves two particles, then I don't see that we're dealing with that in the present example. It's just one electron fired at a barrier.
In the case of a single particle that's either reflected or not, if you insist on looking it as two wave functions, then it's two wave functions entangled with respect to location. And measuring the existence of the particle at one location or the other will cause both to 'collapse' into whatever that position is. It will no longer have any probability of existing at the other location.
So the question is: how has that been verified experimentally?