Molecular geneticist here.
That would be a super sweet experiment

The problem, as I see it (and as a disclaimer, I work with bacteria, not eukaryotes), is getting all the cells in the coral to express whatever genes you want it to at the same time. I don't know of any efficient ways to get eukaryotic cells in an entire organism to take up and express exogenous genes.
Growth structure probably isn't determined by a single gene, nor is the pigmentation. More likely is many different gene products acting in concert to give the growth pattern and coloration. So, even if recombinant DNA is used in this case, it probably wouldn't be as simple as just introducing new genes.
In terms of repopulating the reefs with warmer temperature-resistant coral, the problem is the law of unintended consequences, which is why we keep such a tight reign on recombinant organisms in, say, the food supply. We don't really know what effect being able to grow at a higher temperature would have on totally unrelated aspects of coral growth.
Aside from those issues, I think it'd be a cool experiment. Maybe you should go into that field to work it out
