Does CO2 Saturation Mean No More Warming Can Happen from Increasing CO2?

I sometimes hear that increasing CO2 concentrations cannot cause any more warming because the atmosphere is already saturated with CO2. The idea being promoted is that the CO2 in the atmosphere already traps all the heat it can possibly trap, so adding more CO2 can't trap any more heat. The thought appears to be that the atmosphere is like a saturated sponge. Pouring more water onto the sponge can't add more water too the sponge; water must leave the sponge at the same rate water is added. But this analogy has little do do with the actual physics of how increasing CO2 warms the surface.

CO2 warms the Earth's surface because solar energy entering the earth's climate system is absorbed by the earth's surfaced and is radiated back as IR light (heat). CO2 absorbs IR light at 15 μm and then emits it in all directions. Some of that IR light is sent back to the earth. The more CO2 in the atmosphere, the more IR light is absorbed and emitted towards the surface of the earth. Two important things happen:

1. As CO2 concentrations increase, CO2 absorbs and emits IR light at wider ranges of wavelengths. This is referred to as pressure broadening. So while CO2 eventually cannot "trap" any more heat at 15 μm, it will trap heat at wavelengths on either side of 15 μm. So increasing CO2 still traps more heat and sends more of it back towards the surface.

2. As CO2 concentrations increase, IR light can be trapped at higher altitudes, and the effective radiating altitude is higher and colder, so that means less IR light can escape into space. At higher altitudes, the air is thinner and colder. At higher concentrations of CO2, the atmosphere must be thinner for IR light to escape into space - that is, higher in the atmosphere. And the atmosphere (below the tropopause) is also colder and therefore has a lower emitting power

Increasing CO2 levels to the point that the atmosphere is opaque at 15 μm near the surface simply does not stop CO2 from warming the surface. Increasing CO2 increasingly insulates the atmosphere against the loss of IR light, so the temperature of the surface must increase until the energy escaping the earth's atmosphere matches the energy received from the Sun. In the geologic past, CO2 levels have been much higher and temperatures have been correspondingly much warmer. Perhaps the most dramatic example is the runaway greenhouse effect on Venus. The greenhouse effect there is so strong that its surface is warm enough to melt lead. We're not in danger of that kind of warming on Earth, but the fact remains that CO2 "saturation" does not limit the Earth's surface from warming above current temperatures. The relationshp between CO2 and temperature is still logarithmic. Doubling CO2 reduces the energy escaping the climate system into space by about 3.7 W/m^2, and that creates an energy imbalance  that requires the surface to warm until balance is restored. The central estimate is that the surface warms by 3 C; it could be a little more or a little less, but saturation does not prevent warming from occurring.