It is incompatible with any system of justice if you take the wording seriously and use standard definitions. It would need to be formulated in a way that recognizes jurisdiction and defines aggression less broadly that force absent defense of bodies or property.
If NAP is true, I don't see how arrest can ever be legitimate prior to conviction. I don't see how judging a case on limited evidence can be construed as self defense. What gives a person the right to arrest or harm another person on the basis of uncertain evidence? How is that defense?
Also, if the property definition used by NAP is valid only due to majority consensus, then majority consensus can change the property definition at any time and change which contracts it decides are valid, which laws it will enforce, etc.
You're back to democracy. If the mob defines all property as public, than any law is valid, since violating it is violating the public's property rights and consistent with NAP.