Right. as far as trying to find rational evidence for particular metaphysical theses, it's problematic. In both directions, I would suggest, and for different reasons. Mysticism doesn't disprove a physicalist or naturalist metaphysics, and that is fairly well demonstrated by the variety and contradictory nature of interpretations of those experiences, as well as by their subjective quality.
On the other hand, to use your example, as I understand it, research into NDEs demonstrates some close correlation between certain brain states and certain reported experiences. It's been a while since I read anything on this but I think that's true. And lets imagine that those correlations are even further developed scientifically. Does this disprove that the experiences have some transcendent referent? To my mind, the answer is no, it only disproves the most simplistic and naive kind of metaphysical "supernaturalism". It seems perfectly to be expected that states of experience have to have correlates in physical brain states. I think that's conclusively demonstrated by what we know of minds and brains.
What is not known, and what may not even be provable in this fashion, is that those physical states are exhaustive and that, once described, everything is known. Reductive physicalism as metaphysics can't really be proven in an exact way, any more than supernaturalism can be, although the latter seems rather infeasible. Rather, physicalism is argued towards abductively. It can be demonstrated perhaps that nothing else is needed for a description of physical function, and principles of parsimony can be appealed to on that basis (Occam's razor and the like), but as with mystical experience, the immediacy of the subjective quality of our own experience is something that doesn't seem to easily yield to this kind of functional, scientific analysis. Or at least, such analyses seem plausibly to leave something out, which is no less immediately "real" to us.