In the Elijah case the result came out positive. Of course we can ask whether it happened that way. And we can ask what would happen if we tried to do the same thing ourselves. But the claim is about testability, not the result of the test.
In 1993 the minister Harold Camping predicted that the world would end in 1994. That's a testable claim. When I was young there was a very popular Christian book by Hal Lindsey called The Late Great Planet Earth. It claim that Jesus would return in "this generation" and that a generation is about 40 years, and the clock for that started when Israel became a nation. That's a testable claim. Of course, Lindsey changed is concept of a "generation" and still has a show on TBN. Jesus didn't rapture the Church in 1981 and didn't return in 1988 or anytime close to 1988. If Christ had returned, it would be ridiculous for someone in the fires of hell to say that there is no scientifically verifiable evidence of God's existence.
Do we have a clear enough concept of "the supernatural" to identify ID as committed to the supernatural? That's the question I should have asked first. Are all unobservables supernatural? Philosophies of science have historically limited science to the observable, taking only an instrumentalist view of unobservables. But except for van Fraassen this position has been abandoned.
If "supernatural" just means kind of weird, quantum mechanics and string theory are a whole lot weirder than theism.