As for only buying aqua-cultured corals, wouldn't it be better to only buy sustainably-harvested wild corals so that the coral reefs acquire a direct economic value, which then gives the local harvesters a direct reason to preserve them? If they are only "just pretty to look at", the reefs will loose out every time to other economic interests.
I'm afraid it wouldn't have an impact anyway. You can add up the area of every reef tank in the world, and probably not come close to the area of one fringing reef around one south pacific island. Let's say there are 1 billion people in the world who can contemplate keeping a reef tank, and of those, 0.1% choose to do so-- 0.1% would mean about 5000 reef tanks in Atlanta. Anyway, 0.1% of 1 billion gives 1 million reef tanks. If each reef tank is on average 10 square feet, you get 10 million square feet of reef in tanks in the world. An acre is roughly 50000 square feet, so 10 million square feet is roughly 200 acres. Let's say that if every tank in the world got restocked completely with wild coral every 5 years, you would only have to clear cut 40 acres of reef per year to do so. With coral reefs the size of those in Australia, Indonesia, the South Pacific, Belize, etc, clearly you could sustainably harvest corals for reef tanks forever (frag instead of clear cutting). The Great Barrier Reef covers something like 80 million acres. Somebody check my math, but I think if I'm off by 100x, the conclusion still stands.
Now, siltation, pollution, climate change or whatever might be another matter because they can affect broad areas, but I don't think a blanket statement saying we should only buy aqua-cultured corals is justified as a way to "protect" coral reefs. In fact, by reducing the incentive for locals to protect their reefs (and giving your $$ instead to a company in the US), you might be harming the reefs in the end. But in any case, because the area of the wild reefs is so large relative to the area kept in reef tanks, the impact of only buying aqua-cultured coral would be negligible.