Am I the only person who found this metaphor a bit jarring? It seems very much like the author trying to make himself sound more cultured or intelligent, unless he's trying to say something like "travel with no outward signs of progress."
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".
The top level comment on this thread was saying he found the metaphor jarring - I don't personally find it jarring.
Many say "You are the anvil, and I am the hammer" to imply superiority of the hammer bashing down on the poor anvil. However in reality, the hammer always breaks and the anvil always maintains.