Let's say that it's scientifically proven that ghosts exist. Would they then stop being supernatural and become natural, thus making it impossible to ever have proof of the supernatural?
It would simply move the concept of "ghost" from the realm of unproven and unexplained phenomena into the realm of proven but unexplained phenomena, joining the ranks of other proven but unexplained phenomena like gravity or particle-wave duality. In all of those cases, it would be possible to observe, quantify, model, and predict the effects of the phenomena in our natural environment, even if we don't have a complete grasp of the mechanism by which they work.
Ghosts wouldn't he supernatural anymore, just natural and observable.
And then humans will try to figure out how to turn them into gasoline, and/or have sex with them.