I have seen Neptune buy corals before.
Of course selling to a store will likely get you less then selling personally on the side. You of course pay for the convenience, similar to trading in a car vs selling private sale. Also there is a chance that they may have no need for the particular corals you are bringing in, as they may already have similar ones in the shop. Just saying this to keep your expectations realistic, as selling to a shop is a great option as long as you understand the above.