There are two questions here. Can science address the supernatural? By definition, no. Because if there were discoveries related to "God-science", it would remove those discoveries from the "super" natural into the natural world.
Science has already done that in many ways. No doubt people during the dark ages thought that lightning was from God, and therefore a supernatural apparition. We now know it is electricity, and we now consider it fully within the natural world.
The second question is whether "God", or non-athiesm should be presented in public schools labeled as science. It should not, because it is false to claim it as science when it has not made the jump from "super" natural to natural. And second, religion violates the current interpretation of the Constitution and so is considered illegal in public schools.
I can assure you there are a good many people since the Enlightenment who still think it comes from God. I happen to be one of them. When was the last time science predicted a lightening strike other than ones man, by intelligent design, has brought forth?
Can science address the supernatural? It does so all the time. A better question would be: What qualifications does science have to determine what constitutes "natural" vs. "supernatural?" I always thought science aimed for precision. It sure has a can of worms on its hands if it thinks it can satisfy such arbitrary terms.
And second, religion violates the current interpretation of the Constitution and so is considered illegal in public schools.
That is a problem brought about by those who do not understand what the Constitution means. In no way was it intended to discourage or exclude religious discussion in any and all public academic contexts. If atheistic science is not grown up enough to realize it does not have a monopoly on human knowledge the rest of us will simply gawk in amazement at its capricious duplicity.