"Photosynthesis is a chemical process that converts carbon dioxide into organic compounds, especially sugars, using the energy from sunlight"[1]
If he were using this as a metaphor for the "speed of light" you'd think he'd be referring to the emails going incredibly fast, but what he's actually referring to is his "otherwise spectacular ... assistant" sometimes taking a very long time to respond to emails (because he's busy looking at lulz).
In this case I believe that the author is using "speed of photosynthesis" as a metaphor for being very slow, instead of using the more common simile "like watching grass grow".
I'm not sure if "speed of photosynthesis" is really correct, though - I find it hard to compare "rate of respiration" with "rate of growth" or "rate of email response" but there you go.
He's certainly doesn't mean "speed of light".