I don't think copper would affect the visible cysts....I think it only affects the free floating stages of the parasite? Not sure.. So even if you cure the white spots on the tang there will still be free floating parasites in your main tank...once you put the tang back it will get sick again...
But IMO Melafix or medication by Waterlife is much safer... Or slimpy invest in a UV-sterilizer if you can't stand your tangs getting white spot all the time. UV-sterilizer attacks the free floating stages of the ich parasite.