there are many theories just being put out there. Some people even so far as to make them into products ... heating cables anybody ? Few places go the extra step to get some data and results behind those theories. Fewer get compared to standards to see actual benefits ( see 'liquid CO2' as a source of CO2 ). It's on the people who put the theories out to bring data in support. It sounds like they haven't in this case as well. Back to the situation at hand :
I assume the system you describe is not CO2 supplemented ( at least by a conventional path).
Once sufficient light is available, any available CO2 will be taken up rapidly by plants (within a few hours in lakes with large water to plant mass). Then CO2 from the atmosphere trickles in (depending on how good exchange with the atmosphere is). And that is it basically... the system you describe is pretty much light all the time either plants in tank A or B will rapidly use up CO2, no CO2 will be accumulated overnight.
This is marginally better for both systems taken together in terms of overall CO2 retention as you don't give a long time for the CO2 to degas (at night for tank A). Is that better than having a few extra mg/L CO2 available for the plants in tank A at the start of the day ... highly doubt it but nobody shows data for it. Plus
- in aquariums with active filtration and no CO2 supplementation CO2 from the air is likely the biggest contributor
- sump systems are typically high de-gas systems - whatever little extra gets added will be degassed without a good CO2 injection system
- some plants take up CO2 even at night. It's use by the other tank will reduce their resources.
From a practical point, with the cost of running the light for the second tank you can easily pay for at least a citric acid /baking soda system and get many times more CO2 from it.
This is a graph from Reis , Barbarosa (2014) from a tropical lake but similar trends can be seen for temperate lakes in summer. You can see the CO2 dropping fast within the first 4h (the smallest interval they measured) and you can also see the O2 increasing. With the CO2 conc. the pH will also change. Nature is not stable or in balance, that's what makes it fun.