What kind of copper? It takes 5-30 days to eradicate ick employing copper I think. if it's untreated, ionic copper, 30 pls 30 days for your new fish may be too long at therapeutic levels, plus these are difficult to consistently maintain. I use Chloroquine Phosphate now, but I used to used 4 weeks when treating as a preventative measure with chelated copper like coppersafe or cupramine with is bound ionic.
Fish only system, I think you could add a fish and continue to treat for 4 weeks if it's a gentle copper solution maintained at therapeutic levels, and everyone is eating good. My favorite would be to treat the main tank for your original planned period, and employ quarantine for 30 days for all new arrivals; though I acknowledge this isn't always possible. Harlequin tusk is technically a wrasse I think... I have employed copper with wrasses with no ill effects, but I've heard some complain they are a gentle fish. Your experience may differ.
Before I religiously QT'd, I had ick and velvet each 1 time, and 30 days copper worked, with all fish returned to a 60 day fallow tank with no reoccurace. Perhaps someone with longer term copper treatment could offer some suggestions as to when too long is too long.