Is it possible that, prior to hitting a thermal equilibrium in the atmosphere, the increase in CO2 that humanity puts out every year will come to an equilibrium due to the consumption by the world's plants, which may respond by growing, reproducing and feeding more off of the additional CO2 in the atmosphere at a faster rate?
Yes, with 2 caveats.
More CO2 encourages plant growth up to the local plants' limit. After that limit, the plants are saturated and extra CO2 backlogs into the air. If you intend to prevent atmospheric CO2 buildup, you're better off gradually supplying CO2 rather than deploying it in large surges.
The other caveat is dead trees and other plants that should be harvested or logged to make way for new growth (while providing lumber, fuel, and employment).