No. The greenhouse effect does not work like that.
Let's start over. Let's try to figure it out from first principles. First, what are we trying to figure out? A lot of people think that the global climate is changing. Well, of course the global climate is changing. The closest thing to stability of the global climate has been the recent 800,000 years, maybe longer but we don't have enough data to be sure. We are being generous to call that a period of stability, with five glacial - interglacial cycles included, But, yeah, relative to the enormous fluctuations in even the chemical composition of the atmosphere over the preceding 4 billion years, its been relatively stable. The climate has still been changing but almost repeating, staying within a range around an apparent quasi-equilibrium. It has been close enough to a balanced condition that the very weak and slow variations of the Milankovitch cycles has been enough to influence the timing of the changes.
So, if the climate has always been changing, why the concern now? Starting a couple hundred years ago it was noticed that there had been a glacial period in the recent past. It was natural to wonder why the climate had changed and would it change again. The scientists were off to the races, but the sciences were very young and incomplete. They didn't have the tools or even the concepts needed to actually answer the question. They were brilliant and worked hard but didn't necessarily start off in the right direction. That's science. Let's use hindsight to avoid the pitfalls and look at the view as we stand on the shoulders of giants.
How did the Milankovitch cycles modify the climate? By changing the amount of time that the Earth was spending and at what distance from the Sun. The Milankovitch cycles are variations in the shape of the Earth's orbit around the Sun which changes the amount of energy it receives from the Sun.
How does the energy move from the Sun to Earth? Because both are in a vacuum, the only possible path is electromagnetic radiation. Other conceivable pathways are the solar wind and magnetic fields, but are negligible relative to the electromagnetic radiation pathway. What do we know about that radiation? The popular, but naïve notion is that it comes from the fusion of Hydrogen into Helium. The confusion is natural. The energy does comes from the fusion of Hydrogen into Helium, but not the electromagnetic radiation that carries that energy from the Sun to the Earth. Except for the Neutrinos, all of the energy released by Hydrogen fusion is absorbed in the core as heat, bring the temperature there up to 15,700,000K gradually tapering off over the distance to the photosphere to about 109 times the radius of the Earth to a mere 5,700K. From the photosphere the energy from the fusion of Hydrogen can finally leave the Sun as electromagnetic radiation by the mechanism of black body radiation.
What have we been missing? Everything emits or absorbs black body radiation. No convenient electron energy level transition are required. There are both absorption and emission lines in the spectra of the Sun. But, most of the spectra is a continuous range of black body emissions. OK, the light has to be quantized too, so it is not really a continuous range. But the quantize increment must be somewhere close to the Planck length, give or take a few orders of magnitude.
The energy from fusion in the core of the Sun is finally on its way to Earth in the form of black body radiation with an effective temperature of 5,772K. Then what? Some of the radiation may be absorbed and redirected by some atoms or molecules in the atmosphere, ozone is a good example. A lot more of the radiation is reflected back to space by the cloud tops. For the most part, the radiation reaches the surface, where it absorbed as heat. Some of the radiation is absorbed by the atmosphere, of course. CO2 in the atmosphere does absorb some of the radiation from the Sun and thereby adds some heat, but the amount is small simply because very little of the incoming radiation is at the wavelength CO2 can absorb.
Where does that energy go from there? Remember, the photon that started from the photosphere of the Sun has been absorbed by the surface, whether land or water, and no longer exists. A few select wavelengths are captured by photosynthetic organisms and the energy is converted to chemical energy and some are captured by photovoltaic panels but it all ends up as heat, eventually.
The explanations for how the greenhouse effect works all agree up to this point. The surface of the Earth gets energy from the Sun which warms the surface just like it always has. But how in the world does that account for that heat getting trapped? A common assumption is that since the energy arrived as electromagnetic radiation, it must leave the same way. As if photons were persistent particles. The energy (that was the photons) brought by the photons persist, but the photons do not.
Of course, some of that absorbed energy is indeed radiated back up as infrared radiation. And some is absorbed and re-directed by CO2 molecules. Some of the absorbed energy is transferred from the surface directly to the atmosphere by conduction and other processes that take place at the interface between the atmosphere and the surface.
The common but unconscious assumption that the N2 and O2 molecules that comprise almost all of the atmosphere CANNOT absorb any of the infrared radiation from the surface is just wrong. It is true that they cannot accept the IR as internal vibrational energy of their molecular bonds, but they can absorb it as momentum of the entire molecule. That is because the temperature of the air is often close enough to the temperature of the surface to both accept and emit infrared where the black body spectrums overlap.
So, why does the concentration of CO2 matter? Because the higher the concentration of CO2 in the troposphere, the higher it will be in the upper atmosphere where the CO2 can capture outgoing IR and re-emit it in random directions - including down. That is where the greenhouse effect of CO2 happens. The thermal energy that would have otherwise left the planet is still here.
There is another, less direct effect. The energy not radiated away is then in the lower atmosphere, making it just a tad warmer. Being warmer, the lower atmosphere expands, pushing the upper atmosphere a little higher, resulting in adiabatic cooling of the upper atmosphere. The black body radiation from the N2 and O2 up there is therefore just a little lower and cannot radiate as much as it otherwise would.
Even IF the CO2 effect in the lower atmosphere is saturated, it is not saturated at the top of atmosphere where it really matters.
H2O is confined to the troposphere and CO2 is not. That is a crucial difference. The amount of H2O in the atmosphere is not changing except for the wild fluctuations of the weather. The long term average is maintained by the very large exposure to liquid water over most of the planet. The greenhouse effect of H2O is much like the calculated predictions, keeping in mind that the N2 and O2 in the troposphere also have black body radiation spectra overlapping with that of the surface.
CO2 has little effect in the troposphere where H2O dominates. However, ABOVE the troposphere the situation is reversed. CO2 thins out with increasing altitude, so at some altitude and above, the CO2 cannot be saturated. Up there it can and does capture IR in its spectral range and redirects some of it back down, blocking the transport of some energy away from Earth and to space.
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