Rebecca's response about "completeness" raises a fundamental point. She agrees that she would not teach it in a comp class, but sees it as something she would teach in a "grammar" class. My question is ― can she (or we) convince most English teachers that such stuff belongs in an "English Grammar" class. My guess it that most teachers will find that they have plenty to do in a "grammar class" simply teaching students to be able to identify and discuss the implications of prepositional phrases, subjects, verbs, clauses, and participles. Why do they need to know about these "incomplete" sentences.
     No, I'm not playing devil's advocate here. If, after we ideally have a suggested curriculum, if we find that there is time left (in the students' work), then I have no problems with introducing such linguistic questions. Indeed, the model I have proposed includes the option for twelfth grade of  studying more aspects of general linguistics. I don't however, see the relevance of teaching all students that "John is" is an "incomplete" or whatever else you want to call it, sentence. And remember ― in spite of the tone of my comments, I'm on your side.
Ed