Just because you do not see the ich on their body does not mean that it has not latched onto them. Ich tomites which have only recently attached themselves to the host will not be readily visable. If the fish are indeed healthy, they will fight it off and get it off their body before it becomes any kind of problem. However, in the time being while it was on the body, it was able to host enough to sustain life. Once the tomite attaches to the host, it matures and the 4 stage cycle of ich begins anew.
That is the reason most people recommend quarantining all new fish. Ich can be brought into your tank without you knowing it. If you QT all of your new arrivals, this is reduced almost entirely. If there is any suspect that a fish has ich while you have him in the QT, you can hypo the fish and kill the ich. Possible reasons to suspect ich even if you do not see it on your fish is scratching from the fish and a quick glance at the rest of the fish at the LFS that are in the SAME system as the fish you bought. If any of the fish in the same system have ich, your fish is exposed to it as well and there is a chance he could be carrying it.
(Note: When I say system, I mean any tank that is hooked up to the same filter that you are purchasing a fish from. Most LFS have rows of fish tanks, and each row is its own "system" all running off the same biological filter.)
Here is the scenario. When you take the fairy wrasse out of the display and put him into QT, you will leave your display fishless for 6 weeks. That will indeed kill all the ich in the display, HOWEVER, if your fairy wrasse carries any ich from the display to QT, then the ich is not eradicated because he can just as easily carry it back in when you put him back into the display. This is the reason why you would hypo him in the QT. When you are running the display fishless for 6 weeks, the ich is dying in there because it has no host. When you are hypoing the fairy in the QT, the ich is also dying in there because it has a very difficult time reproducing and sustaining life when the salt level is so low.
Any questions or confusion, please post and I will be glad to help you.