Can light function as a neurotransmitter?
I don't think there is a theoretical reason why this wouldn't be possible.  However, I think there might be some practical problems with a system that relied upon light signaling.  

1) It would be susceptible to interference.  Many bio-luminescent organisms are transparent, so other sources of light could depolarize a post-synaptic cell.  Light also penetrates tissue in organisms that are not transparent.  Blue light can penetrate 2 mm of human tissue and higher wavelengths like red can more than double that.  I could see light acting to replace signal molecules in quorum sensing though.  

2) Neurotransmitters aren't really much of a limiting factor in nervous system speed. A monosynaptic reflex travelling a short distance might take 30 milliseconds, but neurotransmitter transmission is only 1 of those milliseconds.  In more complicated neural pathways, the speed of neurotransmitters might only account for 1/100th of the time.  So, if we're just imagining time-saving nervous system improvement, fiber optic neurons are the way to go.