Yes, I am pretty sure it's the color of the zooxanthellae that gives the zooanthid its color. These algae all have different photosynthetic pigments that absorb and reemit light of different wavelengths, giving rise to the different colors.
My only concern would be the damage to the cells done by the injection. The point at which you inject the cells might be damaged, on a microscopic level, to the point that the substance injected comes right out of the tissue. THEN you have an issue with size of innoculum. I would imagine that at first you wouldn't see any difference, but later on, if you innoculum was large enough, you might see a change.
Basically, if you got enough of the individual algal cells in there and the environment was suitable, then you might get them to grow.
Art, honestly, I am very interested in whether this will work or not but not too optimistic about it. Really really awesome idea!