I've thought the same thing. It would make sense but would be great if someone with real knowledge could respond.
I don't know how much effect that will have, given seaweed is mostly it, but planted aquariums typically need to artificially inject CO2 into the water to get decent growth rates. The exchange rate with air is deeply unfavorable, so there'll be barely any CO2 in the water otherwise.
The exchange rate also worsens as temperature increases. I'm not sure how it'd work out overall.