The short answer is an airstone won't hut anything.
NOTE: the amount of CO2 dissolved in water has no relationship to the amount of oxygen dissolved in water. Water movement will impact CO2 levels though. Just to make the answer even more complicated though, there are some who argue, with valid reasoning, that increasing the amount of water/air circulated through a fish tank might increase both oxygen AND carbon dioxide levels. The amount to CO2 that dissolves in water normally is so much lower than atmospheric CO2 that it might actually help to aerate using an airstone (also - plants use oxygen when the lights go out).
Before I get a bunch of high-tech planted tank folks responding, I'm not talking about those pressurized CO2 tanks, but low-tech tanks and water movement.