I had a yellow tang, a powder blue, a powder brown, a sohal, a clown and a tomini at one point or another in my 75g (I know, most of those dont do well in small tanks but at the time I didnt have a clue) and none of them would eat the caulerpa. I also had some of the calcium rich ones that look kind of like cactus and the real leafy type of caulerpa that looks almost like pine tree branches but I never had any tangs eat them. The only algae growing on the rocks my fish would eat were a red branchy type that they loved, I almost suspect it was some type of gracilaria.
Anyway, just my experience, every fish is different to some extent and probably the number of times you feed and the quantity/quality of the food you're providing make a difference in whether they snack on algae or not. I never had a problem with it and I WANTED them to be eating it, I probably could have cut back on the food I was putting in but I didnt feel good about doing that.