Cleaner shrimp mostly remove dead skin and mucus from fish. They will feed on the larvae of certain parasitic crustaceans, but none that are a problem in captivity. There is no reason to believe that they will eat ich or any other parasites that pose a problem in our tanks. Ich has never been found in their gut contents. The actual parasite is also resting against the bottom layer of the skin, so the cleaner would actually have to wound the fish to get to it. The only time that it's available to be eaten is during the wee hours of the morning when the trophonts are burrowing in. Even when cleaners have been forced to clean at this time they normally wouldn't be, they did eat a few parasites, but so few that there was no statistically significant reduction in parasites on the fish. About all these guys will do for parasites in captivity is pick off the nodules of damaged skin so the fish doesn't have white spots anymore.
But yes, they will clean tangs if the fish lets them.
With 7 tangs in a 125 though, the fish would be much better served by removing several of them rather than adding more to the bioload.