Google To Digitize Much of Harvard's Library
The professor can just wait until the match comes up, and then double-check at that point.
You'd want to do a thorough overview of any potential instance of cheating anyway. A quick run-through would determine whether or not a paper happened to contain an identical sentence clause or three identical paragraphs.
I think the bigger problem would be the second one you described -- that students could plagiarize and then go through each paragraph, changing the wording slightly so as to avoid positive matches. Still, you could argue that this is pretty much what academics is anyway, just with footnotes and a bibliography.