IF you are lucky enough to get one that eats prepared foods you MIGHT get it to live long term. But they are in NO WAY easy to keep in general. Many of these animals take a long time to starve, or die from other nutritional deficiencies.
As an example, Moorish Idols - probably one of the most difficult fish to keep - pretty commonly live a year in captivity, eating all sorts of things, and dying for no apparent reason (probably of nutritional deficiency). Ditto for many seastars and other animals that are actually slowly starving to death while appearing to do well.
But the majority of cleaner wrasse do not do well, most dying long before they reach hobbyists tanks or en masse at the LFS.
There is no reason, IMO, to keep one of these fish unless you have a very large tank with very large fish. They do no service that is not done by other (easier to keep) animals. And I am not sure why the color would be reason to want one (a blue neon goby has similar colors, is a cleaner, and easier to keep).
Also note that there is a mimic of the cleaner wrasse that is far easier to keep (excepting it takes bites out of other fish instead of cleaning them). Very very difficult to distinguish from a true cleaner and much more likely to eat prepared foods.