That's surely going to depend on the details of the non-naturalist view. Epiphenomenalism, for example, makes all the same empirical predictions as physicalism. (Though it might be harder to combine with a "soul" view -- it goes more naturally with property dualism than substance dualism.)

But even Cartesian Interactionists, who see the brain as an "intermediary" between soul and body, should presumably expect brain damage to cause the body to be less responsive to the soul (just as in the radio analogy).

Or are you thinking of "non-naturalism" more broadly yet, to include views on which the brain has nothing whatsoever to do with the mind or its physical expression? I guess if one had not yet observed the world at all, this evidence would slightly lower one's credence in non-naturalism by ruling out this most extreme hypothesis. But I take it that the more interesting question is whether this is any kind of evidence against particular non-naturalist views that people actually hold, like Cartesian Interactionism or Epiphenomenalism. (And if you think it is, I hope you'll say a bit more to me to explain why...)