There is actually a lot of truth to that statement, we climate scientist called it the band saturation effect. David Archer wrote an really good intro chapter into greenhouse gases and has a whole subsection on band saturation effect here if anyone is interestedhttp://forecast.uchicago.edu/chapter4.pdf
. Pic related is the figure that he had on the chapter. This is why climate sensitivity is defined as change in W/m2 energy per doubling of CO2 concentration.
While band saturation effect is true and well known, it is well accounted into all climate models. It is kind of dirty tactics by denier to point out the band saturation effect, without going into the nitty gritty math details of integrating the whole absorption spectra for a given column of atmosphere (which is a fairly complex math to do, not even I remember how to do it because these things are automated in the models).
The bottom line is that there is a reason why 350.org
is a thing. Preindustrial CO2 was 280ppm, and if you assume that you don't want an equlibrium temperature increase of more than 2 degrees C beyond preindustrial climate then plugging into EQ4-1 you'll get 350 ppm as your maximum CO2 limit.
This is a pretty rough calculation given the complexity of a climate system, but it is rooted in fundamental physics, and the layman answer is that yes the effect of band saturation is well known and taken into account in all climate models and policymaking decision