Even if they did produce phytoplankton, which I doubt they do in any significant amount, most corals don't eat phytoplanktom. Clams, leathers, and a few others do, but most eat some size of zooplankton. The size zooplankton they will eat is generally based on their polyp size. SPS
will eat very small zooplankton (frozen food examples would be daphnia, oyster eggs, rotifers, etc.). The larger the polyp the larger the zooplankton the coral will eat, all the way up to some LPS
eating considerable sized pieces of fish or even whole fish.