My only solid answer is to the last question, that copper would not be a problem seeing as how a copper core radiator is copper
My additional concerns:
The only standard water cooling fittings that would even possibly work with copper tubing are the hard acrylic compression fittings, so, are they even OD sized properly to fit normal home copper tubing supply line?
There are 2 types of copper water supply line tubing, the hard copper straight and the soft copper coil, to my knowledge the only one that is bendable is the soft copper and the soft copper does not properly seal in a traditional plumbing style compression fitting without a brass reinforcement insert, so, how well will the traditional water cooling hard acrylic fittings even seal to soft copper?
If the powder coat is an issue you could always tape off each end of the tubing and not have the powder coat on the actual connection area, you'll have to pre-bend the copper tubing and plug the ends of the tubing before powder coating anyway to keep the powder coating out of the inside of the pipe.
The powder coating process uses a electrically grounded process to attract the colorant particles and it will go on and into the tubing if you do not plug each end before the spraying.