To make it simple. Yes. Beyond the shadow of a doubt, and for more reasons than just Ich. If you do not quarantine, but continue to add livestock, the question is not
if you will get something bad, but
when. Everyone that has been in this hobby long enough has had to deal with Ich at the very least.
When it does happen, it is not just a matter of losing the fish that you have, but you can potentially lose everything and start over. You will also eventually purchase a QT setup, so you may as well start correctly. Let me explain how. In a reef tank, there are no completely effective medications that will both kill the parasite, and not damage the invertebrates in your tank, so you will need to catch the infected fish and treat him. How will you treat him? Yep, in a QT tank. Yes, I know TTM and other methods work, but there are costs involved with all, and the OP asked about QT

Say all is going well with your fish you are treating in your new QT, and all of a sudden you notice 3 more fish with Ich in your DT. You have to catch them all to start their treatments, and in the process, you have to move rockwork potentially damaging corals, and you risk the possibility of disturbing a sand bed that has not been disturbed in years. This can cause another mini cycle, and now you are in a situation where your tank has now been completely wiped out. If any corals survived, they are likely damaged during the time you were trying to catch the fish. I know this is a worst case scenario, but it is very real, and has happened.
The moral of the story is to quarantine everything wet that goes in your DT. Period. The lives that we are responsible for are depending on us to do everything in our power to keep them healthy, and a QT is a very very cheap investment.