in this paper, Levitan (1988) observed monthly natural spawning in
Diadema antillarum.
Urchins are readily induced to spawn via injection of potassium chloride (KCl) in the laboratory... sudden changes in aquarium conditions might achieve the same.
It is an interesting question... what's the impact on your water quality. Hopefully your skimmer can take out most of it as the gametes deteriorate.
http://bio.fsu.edu/~levitan/publicat...ology_1988.pdf