It's very unlikely for multiple reasons.
Corals aren't ready to spawn at the drop of a hat. They only develop functional gonads for part of the year, and that development has to be triggered by cues several months prior to the final spawning cues. We aren't sure what it is that triggers that development in corals, but in lots of inverts it's related to changes in water temperature and day length. Most reefers don't let these signals occur in their tanks, so most corals probably aren't even in spawning condition.
Most hobbyists also feed very poorly, which again will have a negative effect on the spawning condition of our animals.
Also, while spawning events are often tied to lunar cycles, there's very little evidence that moonlight is the actual cue. Corals are sensitive to the actual light of the moon, but as a signal it's fairly unreliable since things like cloud cover or rough water can have as big an effect on intensity of the light hitting the corals as the lunar cycle does. Also, corals of the same species on different reefs spawn at different points in the lunar cycle, which suggests that they're not hard-wired to go off at a given intensity. It's generally believed that it's actually variations in tidal strength that are the final trigger.
Even if we were to assume that the corals are in spawning condition and moonlight is the actual spawning cue, aquarium moonlights are unlikely to get the job done. Most of them are orders of magnitude too bright. As a general rule, if you can read by the lights they're too bright to simulate moonlight. Even if you put them on one of the moonlight controllers, most nights will be as bright or brighter than a full moon, which really muddies up the cue.
Blue is prettier 
