For the atmosphere (near sea level anyway), upward flow of energy due to the adiabatic lapse rate would be
P/A = k (dT/dx) = (0.025 W/m*K) * (0.01 K/m) = 0.00025 W/m^2
This compares to ~ 170 W/m^2 of average sunlight and ~ 320 W/m^2 of average incoming thermal IR, along with ~20 W/m^2 removed by convection. The ability of thermal conduction to ever drive the atmosphere to an isothermal condition is completely insignificant. I suspect that the exchange of IR within the atmosphere would be more a significant energy transfer mechanism than conduction, but I haven’t been motivated to try the calculation.
Or put another way, even a few mW/m^2 of cooling at the top of the atmosphere would be plenty to maintain a temperature gradient equal to the lapse rate.