This is not my area, so take this with a large shaker of salt, but I believe being a component unit is an accounting determination, and that determination flows from, among other things, the de facto ownership and control of the separate legal entity. It doesn't dictate ownership and/or control.
If the authority owns the assets, and the city is not the guarantor of any bonds issued by the airport authority, and the make up of the commission is changed to where the City of jackson no longer has the ability to assert majority control, then I would assume it won't remain a component unit (I don't know the actual test but I think it's basically a totality of the circumstances type test of basically is it independent or not). No clue what that means for the city's books for the authority to just disappear from them. I would assume the city of jackson's annual audit has some footnotes about what happens if anybody is motivated to look for it.