No, it doesn't. You've overlooked your own definition, to wit: "...according to scientific method – a process for evaluating empirical knowledge; or The organized body of knowledge gained by such research."
To a scientist, science, first of all, is a method of inquiry. Those unfamiliar with science often cannot grasp this fact and try, instead, to elevate science to a status as being one of the ultimate search for truth. It is not.
Science has inherent limitations and, as such, does not search for truth among the supernatural or non-empirical.
You are assuming what you are trying to prove. Your statement, being a philosophical statement about science, not a statement of science is self-refuting because it is not itself derived from the scientific method (by your own definition of "science"). It is therefore inconsistent with its own terms. Positivism offers no metaphysically neutral ground for disqualifying theories that invoke nonnaturalistic events—such as instances of agency or intelligent design.
Cordially,