Al, I am pretty sure I know what you mean by “CO2 wavelengths”… CO2 absorbs some wavelengths very strongly, and others not very much at all; so I presume you mean those wavelengths which CO2 absorbs. (Correct me if I misunderstand you.)
However, note that there is a continuous variation. One of the major reasons CO2 makes a significant difference as you keep increasing it anywhere along the range from 10 ppm to 100,000 ppm is that the atmosphere as a whole becomes opaque to more and more wavelengths. For example, let us say the atmosphere is “mostly transparent” at those wavelengths where 50% or more of that wavelength gets through, and “mostly opaque” at wavelengths where 50% or more is absorbed. As concentrations of CO2 increase, more and more wavelengths move from being mostly transparent to mostly opaque; this is called absorption in the “wings” or “shoulder” of the main absorption band.
Hence the concept of optical depth is indeed crucial, as you say. However, your concluding inference is back to front. It is the continuous relationship between optical depth and wavelengths which means that you do get a significant and continuous change in the loss of heat from the surface into space (very close to a logarithmic relationship) as CO2 concentrations range over values anything from 10 to 100000 ppm. What we could plausibly see on Earth is all well inside that range.
BTW. The atmosphere heats the surface in the same sense exactly that a blanket heats a sleeper. (Though the physical mechanism is a bit different.) As Vaughan points out, the net heat flows are from the surface to the atmosphere; the surface heats the atmosphere, and the atmosphere cools the Earth. So too, look at the heat flows and you see that a blanket doesn’t heat you; YOU heat the blanket.
You are warmer with the blanket than without, and so in normal speech we do say that a blanket is warmer than a sheet, or than nothing at all. Objections to this usage may be pedantically correct; but I’m still going to speak of “sunrise” for the Earth turning towards the Sun, of being warmed by a wool blanket, and of being warmed by the atmosphere.