With respect to your answer, I suppose it holds true that it applies to more than two gases in a system. Assuming the 'average' heat retention property of the mixture is increased by an increase of a component gas that has a higher heat retention property (in that it absorbs more infrared radiation).
Yes. Where it breaks down are the assumptions that 1) this is an isolated system, and 2) there are no mechanisms of heat retention other than infrared absorption.