I think that's definitely true, although that presupposes that a formal semantics representation exists, which is probably true at least in some sense.
But I don't know whether we need special mappings-- the combinatorial possibilities work out if you assume that "no" can have different meanings in different varieties.
But for the original data in question, I still don't get it. Why does that sentence (more or less) work? Critically, it's ambiguous within the same dialects.