Even if the ich starts to go away on the fish, it doesn't mean that the fish doesn't still have it, the ich is just in a dormant stage. The only way to rid your tank and fish of ich is to take them all out and quarantine them. Believe me, I didn't take the precaution of QTing any of my fish and now I am in the middle of a process of jamming all my fish (including 5 tangs) into a 20 gallon aquarium for hyposalinity because I had an ich outbreak. I am about 3 weeks in.
Especially if you are adding tangs, it is likely they, and your current fish will be temporarily stressed and could get the ich on them. So my best advice is to bite the bullet and quarantine everything or it could hurt you later.
Peace, Poppinthekap
