In a word: No.
Science deals with the physical world. The supernatural supposes that there are unconstant forces that we cannot see, test or measure. That, by its definition, places it outside of the realm of science.
It is not unscientific to say that astrology is not science. It is not unscientific to say that the "evil spirit" hypthesis of disease is not science. It is not unscientific to say that ID is not science. All of them presuppose unknows forces that we cannot measure, none of them address the evidence.
I did not ask if "it" ("it" equalling the supernatural) qualified as science.
I asked if science could judge the validity, or existence, of anything related to the supernatural given that it does not deal in it.
The answer has to be "no"...If science does make judgements or proclamations related to the supernatural, then it is dealing in the supernatural and loses it's scientific status.