Brian
With proper water parameters and care, the coral could still survive. I actually have a colt coral in my tank and notice that it will sometimes droop towards evening before the lights go out. It is also not uncommon for it to droop while acclimating to the aquarium. Drooping in the aquarium is not necessarily a sign that it is unhealthy or dying. You may try placing it in other areas of your aquarium with different water flows and watch for any reaction from the coral.
If you would like to provide us with a picture of the coral, we would be more than happy to review it at which time we can give you more accurate information.
As for the branch, which has fallen off: if this branch is healthy enough, it can be tied to another piece of rock, which would potentially provide you with another coral. If a small portion of the base is not healthy enough, this can be fragged with a pair of sterilized scissors and then attached to another piece of rock. I have used 20-pound test fishing line, tying it just tight enough so the coral will not fall from the rock, but not too tight that you are cutting into the flesh. Please keep us updated with the progress and health of this coral. If you have any further questions, please feel free to contact us again.
Leah B.
LiveAquaria.com