Actinics are not just for aesthetics.
The dual actinic bulbs used in most systems have one bulb that peaks around 420nm and another that peaks around 460nm. Light in this area of the spectrum is also used in photosynthesis.
Chlorophyll A and Chlorophyll B both have absorption peaks between 400-500nm. Both of these types of Chlorophyll are present in zooxanthellae, which are the symbiotic organisms present in coral.
To be specific, Chlorophyll A has a peak closer to the lower end roughly around 430nm, while Chlorophyll B has a peak somewhere around 460nm. I can't give you specific numbers, because determining that is complicated. The solvent used to extract the chlorophyll for scientific studies affects the absorption spectrum.
Anyway. I hope this is a good enough explanation. In short: good actinics = good photosynthesis = good coral growth