Having just read through this entire thread, I'm forced to note that the topic really can't be discussed, because nobody agrees on what the definition of the terms being used really are.
What is "supernatural?" If something like telepathy exists within nature (even a "fictional nature"), doesn't that make it NATURAL?
Much of what we recognize as science today would have been treated, and not irrationally so, as "supernatural" centuries in our past. Magnetism... broadcast communications... computers... how many things do you, personally, own today which utilize things which people just a couple of centuries ago would have led to you being accused of "witchcraft?"
For this reason, I'm disinclined to accept the term "supernatural" as having ANY meaning. When people refer to "supernatural," they usually mean one of two different, and entirely unrelated things:
1) Nature which is above the "mundane" nature we already recognize,
2) Hoaxes and lies.
Those are the "pro-supernatural" and the "anti-supernatural" positions.
The thing is... the first one is bogus, because anything that exists within nature isn't "supernatural," it's merely "nature we don't understand yet." And the second one is bogus, since "not knowing something" doesn't mean it's necessarily not true... as the cell phone in your pocket (a "witches tool" if seen in the 1500's) is recognized as working within (not "above") nature as we know it today.
The real meaning of the question, then, is "does any science fiction make use only of science we already understand," isn't it?