No, that's not how non-determinism work.
You can think about non-determinism as parallel universes. All the branches runs concurrently, in a different plane, and to itself it seems like it's the only run in the world.
The language accepted by a non-deterministic turing machine is every word that there exists a universe (or respectively a run) such that it gets accepted in it.
So in that sense, non-determinism means run all the possibilities, and choose the best one.