Answer:
No, because xanthophyll dissipates absorbed light as heat, and in low light environments, such dissipation would decrease photosynthesis and therefore growth.
Step-by-step explanation:
Xanthophyll is one of the accessory pigments present in organisms. Being an accessory pigment, the function of xanthophyll is to dissipate the absorbed visible light. Since it dissipates the visible light, the light cannot be used by Chlorella to drive the light-dependent reactions of photosynthesis.
When a mutant Chlorella is grown in the shady region, the dissipation of light by xanthophyll would further reduce the rate of photosynthesis. This mutation is not an adaptive feature in shady regions where the rate of photosynthesis is already lower due to limited availability of light and therefore, would not be favored by natural selection and would not spread to the future generations.