Paint a sphere black, and it gets hotter than a white sphere. Emitting CO2 makes the Atmosphere "black" in the infrared, thus you increae the energy input to the system.
If the local effects have a little bump or not does not matter to the fundamental equation.
Nowadays we use modeling with great success. The models which were used to procude the processors you type on are complex. The planes you fly in are modelled. The controller in the stabilization system in you car was modelled.
Should you severly doubt that for something (globally long >100years, not locally) as simple and an energy conservation equation is not reliable, is suggest that you dont use a plane, dont use a car, and move into the forest.