And doing nothing would have either ended up with a dead Tang or a Tang that appears "Ich free". Those little white spots drop off as part of the life cycle. Some, that are free-floating, will get caught by the UV
( if it was set up properly with proper flow). Others will almost surely have dropped into the rock and/or sand and are incredibly happy to know that they were not "cured" and will live to fight another round with your fish in the future.
Copper or Hyposalinity, paired with a fallow tank, are the ONLY cures for Ich. Anything less ensures that the Ich lives on in your tank. It could be months for it to increase to levels where there is a good chance of another fish catching it, but the odds are against the fish and in favor of this annoying parasite.