Well, according to LA they are with caution because they are not entirely invert safe.
"It will eat fireworms and pyramidellid snails, protecting corals and clams. In addition, it may eat feather dusters, wild shrimp, tubeworms, and flatworms. It may also eat parasites off of tank mates. The Christmas Wrasse diet should include vitamin enriched frozen mysis shrimp, vitamin enriched frozen brine shrimp, and other meaty foods along with a high quality marine flake and marine pellet food."
Looks good for corals and clams.