Not exactly. If outward radiation from any part of the surface or of the atmosphere is not absorbed on its way out, it will leave the earth. If it is aborbed, it will be re-radiated and 50% of it will be radiated back toward the earth. If above certain level the atmosphere did not contain any molecules that could absorb outward radiation and below that level the molecules absorbed ALL the radiation coming from below, the temperature of the atmosphere at that level would be the blackbody temperature of the earth. But the atmosphere is not like that.That's, right they don't. But the keyword is emission altitude. (sorry short in time right now)Mind that if the incoming radiation is worth a blackbody temperature of -18C then at radiation equilibrium, the outgoing emission must originate from the same temperature range. No?
Radiation emission orginates from all different levels at all different temperature ranges. Generally, the atmosphere is at thermal and radiation equilibrium at all altitudes.
The radiation distribution (the graph of intensity of radiation as a function of frequency) as seen from space will be the Planck curve corresponding to the blackbody temperature of the earth. That never changes (unless the emissivity of the earth changes, which is a function of the earth's albedo). What changes is the altitude in the atmosphere where the temperature matches the earth's blackbody temperature. As the atmosphere warms, the altitude at which the air matches the blackbody temperature of the earth increases.