This is really not recommended. There are customs problems (even for DEAD coral skeletons)...I know of
museum specimens that were dead that were seized for improper CITES (endangered species) documentation.
On a more philosophical note...isn't it just nice to leave some areas natural? The take nothing but pictures/memories and leave nothing but bubbles? They already are under HUGE stress from hurricanes, divers, boating, overfishing (when I went to Jamaica in the 80s, man, was it devestated by hurricane damage)...does it really save that much money or whatever to go take some coral from there too? Especially for something that is so common and easily cultured in captivity like Zoanthids and mushrooms? I think it is worth thinking about.
Since it may very well come up, I won't buy the diversity argument. There is nothing valuable, IMO, in throwing Caribbean species in a tank with Pacific one's and claiming diversity. And for the "they do it for the LFS animals so why not." Your right, and it causes enough damage which is why we are trying to promote captive raised animals. Why spread it even further around...especially for something common.
Also keep in mind that much of the coral diversity you are familiar with is Pacific. Caribbean reefs may seem much different. Unless you are SCUBA diving, I don't know how often you will stumble upon great patches of zoanthids and mushrooms to harvest but their is amazing algae
Serious!
I know you don't mean anything by this, it seems harmless for sure, I don't want anyone to think I am flaming. I think it is just something to think about even if customs says it is A-OK (which I doubt). What is the reason for doing it and is it really good. But it is just my opinion, no flaming...just philosophical on my Friday.