By that argument almost any exclamation can form a sentence - including non-words such as ARGHHHH !
Here are my final thoughts on the matter:
App103s original question is "No!" a sentence is probably best answered by it can be. As I understand the English lanuage, as I stated earlier, this is the command form of the language. The subject (you) is implied by the individual speaking to whom the speaker is talking or to whom the speaker is commanding. If "no" means desist as in the example I gave, then it is a verb and then sentence, if in written form could be taken as "You stop" where there is a clear subject and verb.
When there is no subject and the verb is a non-word, it is a very different case. I already indicated, through referencing Webster's dictionary that No can be a verb, whether common or not. I also find this example very similar to the example of a one word sentence from Webster's dictionary "Stop!"
If my first example wasn't clear enough. Here's another. A would-be mugger/rapist moves toward a woman. She screams at him. No! The thug moves off concerned that her scream will bring unwanted attention. Here the implied subject is the thug. No, as in my previous example is used as desist, stop (like Webster uses), or quit. Hence, as in all the other examples I have given, we have a subject and a verb, the minimum requirement for a sentence, even though the subject is implied.
While this might be an unusual and perhaps an infrequent sentence in prose, that does not make it agrammatical or not a sentence since it meets the minimum requirements for a sentence (at least according to my and Webster's understanding of the language).