I dont think it would bring in more C02 but instead more 02. Although if you are talking about circulation then it would move the C02 around the tank more moving it to all the plants. 02 is important for many chemical reactions in the tank and in assisting in C02 absorption to my understanding.
There is a certain equilibrium between the CO2 in the atmosphere and the CO2 in a fish tank. I really have no idea what that level of equilibrium is, but probably very low -- like 2 - 3 ppm CO2 will naturally dissolve in water before a state of equilibrium is reached and stays there. CO2 dissolves into water very easily (much easier than O2). I'm guessing that high surface turbulence will move that water's CO2 level to equilibrium at a faster rate. The thing is the turbulence will bring in CO2 if your CO2 level is below the equilibrium level (i.e. your plants are using it up), BUT, if you are over the equilibrium level (i.e. you are injecting CO2 or your fish are producing it), this turbulence will LOWER your CO2 level more quickly.
A more effective way of getting your CO2 back to equilibrium level would probably be to inject air bubbles into your tank ... and, to make it even better, chop those air bubbles into microbubbles.
Either way, you are stuck with a low CO2 environment, unless you inject CO2.
Of course, it's still a very good idea to have surface turbulence, because it brings more oxygen to your fish and other critters.
If there are any errors in my assumptions, someone please correct me.
Air is about 80% nitrogen, so logically, surface turbulence would increase the amount of dissolved nitrogen in the water. Except as Ted noted, the water will already be in an equilibrium with the nitrogen in the air, and none to speak of is used or generated in the tank, so the turbulence would have no effect at all on nitrogen in the water. But, both oxygen and CO2 in the air may not remain in equilibrium with that in the water because both are used/generated in the tank. So, surface turbulence would help keep both at the equilibrium value. If the plants are using the CO2 in the water, and if they are growing, they are doing so, then surface turbulence should be helpful for providing CO2 to the plants. For low light tanks I would expect this to be of some value. Probably not a lot of value, but certainly some.
They still have circulation(some remove the filter is some twisted notion that the reduced NH4=> NO3 conversion that the filter does will help the plants grow better-this does not, the roots and sediments do this much better and have far far more area than the puny little filter when plants are well established- unless you address that, that entire theory is tossed out the window) ...............but some have argued this without ever testing the CO2 critically. It's low in these systems makign much harder to tell what is going on.
Too low for any hobbyists methods of measurements.
So it is still speculation. Growth rates comparisons are also painfully slow since things are CO2 limited. So any data is pretty scant. My take on it is more centered around CO2 mist. If you have mist, whether it's air or pure CO2, or something with a % of CO2, that hits the plants, even if the CO2 is very low, this will help. You cannot use O2 measurements for measuring plant growth except in stiller waters, since that will get blown off rather fast.
I've seen a lot of nice plants doing quite well in streams with waterfalls and current. Not enough to uproot them, but in slower flowing sections.
This tend to do best with lots of mist in the clamer waters below the torrents.
CO2, current, still water has more time to expose the leaves to nutrients?
I'm not sure.
Ole Petersen might know or may have tested something like this.
We have 2 things going on here. One is the production of CO2 from within the system(autochthonous), but this is entirely dependent on O2 from above and the plant's internal production of O2 to the leaves and transport into the root zones-there's that big NH4=> NO3 filter), and this can be a fair amount...............but it is entirely dependent on O2 from above and outside the system and also the O2 produced by the plants.
This is not just about CO2, O2 is used in aerobic respiration to produce the internal CO2, it has to.
This aspect is overlooked but is critical, we keep fish and want a steady supply of CO2.
Adding O2 mist via the air and some CO2 might do better, I'm not sure. Seems that some current is a must for adding O2 to drive enough so the fish do not gasp and the bacteria can cycle the waste. Recall that non CO2 tanks do not get a lot of water changes if any for many months. All that waste must be processed well and at a decent rate.
It takes O2 to do it.
I think some folks have over aerated their non CO2 planted tanks in the past, perhaps a CO2 mist level of aeration, a small mist amount would work better than none or the too much example above.
I'm not sure.
Have not tried and have not measured CO2.