Gotta slightly disagree with nde's simplification... I think the short answer is "yes", because coral skeletons are made from calcium carbonate. :) without carbonate, LPS and SPS cannot grow, like Yote said. However, if you've only got softies, alkalinity is less important... except that's what maintains pH stability.
sorry nde, just don't want people to think things are simple. :-P
I realize you're a chemist, but I don't think you understood the bulk of what I said. A simplified version of what I previously quickly explained is below.
"Alkalinity is a complex measurement. It is not a "thing" in the water. It is actually the summation of many things, all of which together provide a particular chemical property. The reason that aquarists measure alkalinity is that in normal seawater, most of it consists of bicarbonate and carbonate. Bicarbonate (HCO3-) is what corals take up and process into carbonate (CO3--) in order to build their calcium carbonate skeletons. Consequently, alkalinity is an indication of whether or not adequate bicarbonate is present in the water.
Normal to high alkalinity implies adequate bicarbonate, while low alkalinity implies that it may be in short supply. In the absence of any method of supplementing alkalinity in a reef aquarium, the water can rapidly become depleted of bicarbonate. Alkalinity's depletion from normal to unacceptable levels can take only a day or two in some reef aquaria, although it can take longer in aquaria with a lower demand for carbonate. When the water's bicarbonate is depleted, corals that deposit calcium carbonate can become stressed and even die. I recommend that reef aquarists maintain an alkalinity of 2.5-4 meq/L (7-11 dKH, 125-200 ppm calcium carbonate equivalents)."
A Simplified Guide to the Relationship Between Calcium, Alkalinity, Magnesium and pH by Randy Holmes-Farley - Reefkeeping.com
As you can see, we measure alkalinity because it gives us an idea of the amount of bicarbonate that is present in the water. It is extremely difficult to test for present bicarbonate with a home test kit, thus we check the alkalinity. PH is also tied closely into this, as levels of carbonate and bicarbonate effect the PH.
"Much, though not all, of the carbon source for calcification comes from external bicarbonate. As the alkalinity is reduced (at a given pH) the bicarbonate concentration (which comprises the bulk of the alkalinity in seawater) will also be reduced. Diffusion of bicarbonate or diffusion of CO2 from the coelenteron can apparently become rate limiting in many corals."
Chemistry and the Aquarium
Alright, so what's my point? Obviously maintaining proper alkalinity in your aquarium is KEY to the success of all corals, obviously SPS and LPS the most. But the question at hand was whether or not alkalinity DIRECTLY affects coral growth/calcification and all that... and to that the answer is "No."
Does this make sense??