They would have no basis to strike down Chicago's law without incorporating.
I don't know. As of today, they could. Evidently, the President of the United States is also the Mayor of Chicago, and the President of the Chicagoland Chamber of Commerce, as well as the city's delegate to the International Olympic Committee.
One could argue that, however the 14th Amendment impacts the 2nd Amendment in other parts of the country, the government of Chicago is indistinguishable from the Federal Government.