You do not want to dose copper in a tank with inverts. Not even temporarily. Setting a QT would be the best method for counteracting the problem. Of course, you could invest in a sterilizer or start lacing your foods with garlic and vitamin c to boost the fishs' immune systems. I would go that route instead of copper. Copper is for badly infected fish with advanced parasitic infestations and/or lice, etc.
If you treat your tank with copper, some might stay in the tank and I have heard that silicone might absorb it and keep it in there. If a tank was treated with copper, I would never, EVER use that thing ever again if planning on a reef or invert tank.
If my fish came down with a sickness, copper would be my last choice for treatment, too dangerous for my precious animals in my coral reef. The best way to prevent stress is water changes, feeding nutritious foods full of garlic and vitamin c.
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30g reef tank, CPR CY192 filter w/ DIY plumb running Rio 17HF return, Coralife 3x 9w UV Sterilizer, 3 24W T5-Helios 10K Daylights/3 24W T5-Helios Blue lights, 2 Logysis blue meteor light strobes (moonlights/24 Blue LEDs).
Tiger tail cuke, asst. snails/hermits, asst. feathers, rainbow acan,zoos,shrooms,bubble,galaxea, asst. shrimp, 2 ocellaris,mandarin,zebrasoma xanthurum,pink-spot watchman,red-striped pistol. | 
Possible sick fish with inverts. 
dang lazy cleaner shrimp! 
