No-one wants to take on my challenge to guess the impact of water clarity on lighting in an aquarium!
My measurements show that the impact of water clarity on light transmission is not all that high. See:
Light transmission in aquarium water: How important is water clarity?. I found that the loss in irradiance from air (and you aren't going to get water that clear) to yellowed old aquarium seawater was less than 20%. The increase in irradiance from the old seawater to air was less than 25%. The actual losses in a tank will be less because even with ozone and carbon you would not have water as clear as air.
A change in irradiance of 25% will cause no more than a 25% change in the gross photosynthetic rate. This is because the curve of photosynthesis versus irradiance is initially a straight line (at low irradiance). As irradiance increases, the rate of change in the photosynthetic rate decreases and so the impact of the change in irradiance could be much less. Such a small change in irradiance is likely to only cause a small change in the density of chlorophyll in the zooxanthellae. This will probably be too small to even be detectable as a change in colour of the coral.
An immediate increase of irradiance of 25% is not going to cause bleaching, unless the coral was already stressed. There have been numerous studies into photoacclimation in corals with increases in irradiance far larger than 25% and the colonies do not usually bleach. In one study,
Stylophora pistillata colonies adapted to shade (10% of surface irradiance) were placed in full sunlight (100% of surface irradiance) and there was no bleaching. That's a 900% increase! Further, it would be difficult to cause an immediate increase in water clarity, other than doing a 100% water change and then it would be the water change that would cause the stress and bleaching.
An increase in zooxanthellae density due to elevated nutrients is unrelated to irradiance changes due to water clarity - although the two may coincide. Further, an increase in zooxanthellae would not cause the coral to fade but would make it darker. Certainly, it may become more brown and so appear less colourful, but that is not fading.
The function of coral pigments is not known. It has been suggested that fluorescent (GFP-like) pigments may be photoprotective and there is some evidence to support this. There is also conflicting evidence such as two colonies of the same species side by side receiving the same irradiance and one has GFP-like pigments and the other does not. If you assume that the GFP-like pigments are photoprotective, changes in irradiance may influence the density of the pigments. However, a change in irradiance of 25% is likely to have little impact on the coral and little need for a change in photoprotective pigments.
Pocilloporin (the pink pigment in pocilloporids) and the pocilloporin-like blue found in acroporids has been shown to not be photoprotective, UV protective nor photoenhancing and so there is no reason that changes in irradiance would make any difference to the density of these pigments.
What is a "photoilluminating color pigment"?