I do not not think that it is impossible for science to demonstrate the need for an intelligent designer.
Bring empirical evidence. Your need does not constitute empirical evidence. And all of these scenarios that IDers come up with, that can just as easily be explained by natural means, do not constitute empirical evidence. See, for example, Behe's testimony at the Dover trial. He ended up with heap big egg on face because he was pushing a religious belief (disguised as irreducible complexity) and ignoring scientific explanations for the same phenomena--and those scientific explanations came back to haunt him. (You can't just ignore data when its inconvenient, as creationists are wont to do, as inconvenient facts don't just go away no matter how much you ignore them.)
Especially if an intelligent designer (i.e.God) has told us a plausible explanation for why the fossils exist as they do (i.e. the flood)? How is this not science? It is both testable and falsifiable.
1) To the degree that it can be tested by science, the biblical flood hypothesis has been falsified. The early creationist geologists, seeking to prove the flood, gave up nearly 200 years ago in the face of overwhelming geological evidence that the flood story could not have happened as described. Since then the evidence from a variety of different fields has led to the same conclusion. So, don't try to use the "plausible explanation for why the fossils exist as they do" when that explanation has long since been falsified by science. (Of course there are some who, for religious reasons, refuse to accept the evidence but that doesn't constitute proof of any kind.)
2) The intelligent designer is not "God" as that would make ID into religion instead of science. The intelligent designer, if such exists, must remain unknown. (Didn't you get the memo?)
Religious belief does not constitute scientific evidence, nor does it convey scientific knowledge.