There are a couple of things that can happen depending on the coral species. In the case of photosynthetic SPS
varieties, you might see less polyp extension which may or may not affect the corals speed of growth. I have some Acros that I hardly ever see the polyps and it grows really fast anyways.
The worst thing is bleaching, which some hard corals can recover from, but it generally kills them. So it's safer to start out with the LEDs either dimmed if they have a PCM driver, or shade the corals with something at first, then gradually expose them to the stronger light.
Mushrooms will extend a bit smaller at first as they realize they don't have to hang it all out to get enough light density for their algae. Some soft corals like Xenia will extend shorter, again as a result of not having to reach for the light.
corals seem to not care one way or the other.