I tried to kill bugs that way and it was totally ineffective for me.
I'm not so sure that CO² is only for green shoots. CO² is plentiful underground, being a byproduct of decomposition. Plants like decomposing things, so there has to be a reason. I don't think it's mere coincidence.
Roots have no use for co2 at all. Co2 is needed for photosynthesis which is absorbed thru the stomata. Roots use carbon and decomposition which converts carbon and sugars into co2 which is emitted in the atmosphere.
When co2 is added to the roots it starves the roots of oxygen which creates an anaerobic environment where pathogens and bacteria take over and kill roots by decomposition.
Co2 is not for your roots its for your plant to convert into energy which increase metabolism that allows the roots and plant to absorb more water and nutrients. Co2 is absorbed by plants thru leaves and oxygen is used by roots and its by product is co2 which is release into atmosphere.
If you have a reservoir w water and agitate it by circulating the water with a pump or airstone its beneficial for your roots because it releases the co2 and increases the oxygen which is why its beneficial for your roots. If you put co2 into your roots you would choke out the roots by depleting the oxygen. So co2 is not for your roots its is detrimental to their health.