With the s-b law it´s easy. The star emits according to temperature, with a source power density according to the inverse square law. You add the gas-shell and let it come to a steady state of emission and convection, Q+W. The temperature difference of the star and the cloud determines the potential for heat flow according t the s-b law for heat transfer. So, in any case, it will be a transfer of energy into the colder gas, and heat transfer from the star. This is the only exchange there is. One might argue that energy flows back and forth in ways not included in the s-b net transfer, but that is irrelevant for heat flow. The net transfer is what we can calculate. There is no hidden heat.
So with an added gas or atmosphere, the same amount of energy is used to heat a bigger volume simultaneously. The star emits $T^4$, and also transfer $T1^4-T2^4$.
Adding mass to a constant limited heat flow means less energy per molecule. Therefore you will not have any addition of energy from the radiating layer of gas, only a diffuse reduction.
$T^4$ is a measure of energy density. When using the s-b heat transfer equation you balance the densities of different temperature regions. It´s just like how you mix different concentrations of a solution. They don´t add to each other, what you get is dilution.