Unless you go to a place specialising in vehicle wheels, most powder-coating places won't do anything with the tyres. They'll want the wheels bare, without bearings too. A lot of powder coaters do quite industrial stuff like 20' iron gates, and won't have the facilites/skills for replacing tyres.
Take them to a tyre place, or bike dealer and pay about £5 to have the tyres taken off. Once the rims have been painted then take them back to have the tyres put back on and balanced for about £10-£20.
NC30 roadbike- work in progress. NC30 trackbike- work in progress.