yes, it does come off, the form you actually "see" is usually only on your fish visible for a week, then falls off and starts the cycle again. Basically, unless you are only going to QT EVERYTHING you ever add to your tank, corals, inverts, chaeto etc, keeping ich out of your tank is dang near impossible. So the answer is, to keep it at bay. You do that by, feeding a wide varied healthy diet using garlic and selcon sparingly, unless during an attack. Keep stocking levels healthy and low, IMO that fish gets too big for your 125 and is prob one of the most ich prone fish out there(prob 95% of ich threads are because of a tang, and usually that one, a YT, or a Naso), but I digress, jsut keep feeding it well and read up on hopsital tanks, they are cheap to set up, but a PITA to keep params stable. I'd suggest starting a mechanical filter on your DT to use for a future QT/hopsital set up. It allows ya to grow some good bacteria to help keep params stable in a hospital tank after ya switch the filter over, I just use an old filter, add rubble to it and then have it to transfer over if needed. Thankfully, I've never had too.
Not sure what the rules are for posting a link to another reef site, sorry and feel free to delete, but this is an old ich thread I created that has alot of good info
ICH 101 For the Noob by a Noob