For reference, which coating and what wax are you working with? How long was the coating on the paint before you waxed over it? A lot of coatings can handle things like lighter spray waxes and not be too negatively impacted, but applying something like a heavier paste wax is not something that I would recommend. It may not destroy the total protective layer of the coating, but that top surface of the coating that gives you that great hydrophobic performance may be permanently affected by just the physical act of waxing on top, depending on the kind of wax. If it's not damaged during the application process, it could take some time for the coating to shed the wax off naturally, but I agree with the others that trying to target just the wax specifically for removal could harm the coating in the process. We could run some tests, just need to know what you're working with.