Zooxanthellae are brown, or golden in color, so they won't turn your coral red, blue, green, pink........... It is the genetics of the particular coral that determines what secondary pigments it's capable of producing. Some corals are only capable of producing one color. Like elegance corals. They can only produce green. Some other corals are capable of producing multiple colors, but only in particular areas of the coral. Giving them a patch work appearance. This is common in "brain" type corals like Trachy, and Acan. Still other corals are capable of changing their secondary pigments in response to changes in the environment. Like PAR, and spectrum of light. These corals will still be restricted to those colors they are genetically capable of producing. This is common in some SPS corals. I once purchased a bright green Milli, and after a few weeks in my tank it turned a florescent orange in some areas, and bright red in others. We have no way of knowing what color changes may occur in a particular strain, of a particular species, unless someone has documented these color changes in relation to PAR, spectrum, and to some degree nutrient levels.
Generally speaking, in most corals, we can expect secondary pigments to become more intense as PAR increases, but we have no way of predicting color shifts, like green to red, without prior knowledge of the particular coral.