Can Bioluminescence drive photosynthesis?
Yes and no. Yes as in the energetics do work out and you will be going down a small but non-trivial driving force as long as you continue to provide the luciferin to the algae.

However, the wavelengths of light by which photosynthesis absorbs its energy are well defined and narrow. As a result, light sources for photosynthetic organisms have to be fairly strong and bright to cover the whole spectrum to provide the necessary light. As a result, your bioluminescent algae will also have to emit light at the desired wavelength to achieve a high photochemical efficiency and provide light to both Photosystem II and Photosystem I which have different wavelength requirements.


(source: gsu.edu)