If Earth received less solar radiation, would its atmosphere decrease in altitude?

Yes. To be more precise, a graph of altitude v. pressure would be lower, and the altitude below which any given percentage of the air resides would be lower. That would be a consequence of the air being cooler. As the average height of the air decreases, there would be a corresponding heating effect; but that would only slow the cooling effect very slightly. The decrease in altitude of the air would have much less effect than the lower temperatures, but it might mean less precipitation on the highest mountains and more at lower elevations.