I don't know if this helps, but I had a friend bring me a cleaner-shrimp from Miami to RJ. Brazil.
You have to put "live animal" in clear plastic bag and declare it at TSA, but they will let it through. Make sure you have the receipt of where it is purchased and also documentation that it is NOT on some endangered species list. Anyway, my friend did everything the proper way and TSA gave him no issues.
What I would suggest would to have an insulated, styrofoam bag/box to put the coral into after you had declared it. Personally, I think you will be fine just do a little research about India's import laws.