I agree with naruto that this is not incorrect, but is inappropriately blunt.
We can understand this without reference to historical Japanese, and thinking about language in general terms. Cross-culturally, formal language tends to put more emphasis on the recorded semantics of the words themselves; informal spoken language tends to put more emphasis on intonation (and informal written language will often try to convey that via eye dialect).
ません is a formal negation; it makes sense to expect か in order to distinguish a question from a statement. (Of course, it is still left to the listener to parse the negative question as implicitly an invitation.)
ない is informal; as such, it is expected that the listener will decide whether this is a statement or a question by intonation. Adding か, therefore, carries the implication that specific, heavy emphasis on the fact that it's a question is somehow needed. It will come across blunt or pushy because of the implication that the listener might otherwise ignore the question.