First, spray paint will not last for more than a few miles. It will start chipping off, getting junk in your drivetrain and looking worse and worse. I believe the colored chains you see are powdercoated, not painted.

Second, breaking and reassembling a chain at every link is pretty risky, especially since you don't seem to have any experience with a chain tool. In particular, you are assuming that you can remove the rivets from both sides of the outer plates in order to paint them. If you do that, you will have a very hard time getting the rivets back in.