Science is merely the study of the natural world, and from a Christian standpoint, a study of God's Creation. It does not, and can not, explain anything supernatural. You are all right so far.
But, science *recognizes* that it can not account for anything that is supernatural, and does not try to do so. As a discipline it does not preclude the supernatural, it is simply not equipped to deal with it, and so doesn't.
And yet, it's job is *still* to do the best it can in describing the natural world around us, even with this accepted and known "blind spot". So, it goes forward and observes, tests, theorizes, at best it can.
And, yes, this will mean that it will, on occasion come across an event actually *had* a supernatural cause, and will be attempting to explain it naturally. This will, of course, lead to a wrong conclusion. Any scientist would acknowledge this, but point out that they do have to go forward since they can't *assume* a supernatural causation.
And, even we as Christians would not want them to. There was a time when Christians (and all religious groups) assigned supernatural causes to all kinds of natural events (demons which were germs, rainbows, etc, etc) and it would have been incorrect for science to have avoided researching the possible natural explanations for those things just because some saw them as supernatural events.
More often, though, the supernatural is not a refutation of the natural laws that science discovers, it is simply a singular *over-riding* of those laws. Science is still correct when it says that Man can not be raised from the dead as a law of nature. God just chose to over-ride that law (which He created anyway) in a given instance.
As for evolution, the problem is that we simply don't know (and no, the Bible doesn't tell us) the degree to which He used natural processses to complete His creation. Science provides us with evidence that indicates that life evolved a certain way. We, as Christians, would say "well, if that is true, then obviously God did it that way." A denial of scientific conclusions is not the only possible Christian response.