The claim that dualism's existence requires interaction with the nervous system itself requires the assumption that the mind and body are fully connected, and thus, is something of a silly claim to make. For instance, assuming instead that the mind does not arise from the body alone, the effect could just as well be similar to a neural network, with the soul and the body, or various parts of the soul and the body, providing inhibiting or exciting impulses.
If this were the case, and I'm not saying I find it likely, neuroscience would have no way to detect or account for the phenomenon. For all intents and purposes, neuroscience would keep on correlating behavior, reports and so forth to various outputs as if nothing was amiss, seemingly getting ever closer until some day everything was neuroscientifically accounted for and the puzzle pieces still didn't quite fit - at which point one could begin to investigate the pattern with which they didn't fit, so to speak. Thus, it would certainly be functionally invisible, as would any number of other scenarios.