Nope! We would not give you advice to medicate your future reef tank with copper! :) But it's a good thing you thought to ask!
The medication is harmless to the other stuff in your tank, and you only need to inject the aiptasia itself, so very little (if any) gets in the water.
Like Sniffles said, peppermint shrimp will take care of them naturally if you prefer to go that route (which I think is a better route anyways).