You are broadly correct. Agitation encourages gas exchange with the atmosphere, and since densities of both O2 and CO2 in the water are usually much lower than their atmospheric densities, O2 and CO2 will usually show net movement into the water. Now, there's no such thing as a saturation point in air, but the relative proportions of the gases that make up air are fairly consistent.
Here's the exception: CO2-injected systems keep CO2 levels in the water at or above the saturation level, and agitation causes these levels to drop. It may not be practical to have enough agitation to replenish CO2 as quickly as the plants in these systems use it. You may ask how these plants survive in the wild; in many cases these plants are not true submersed species but submersion-tolerant emergent or marginal plants, which are not adapted to low-CO2 aquatic conditions.