They do, indeed. For, if they are "colorless green," the ideas are ones of envy or jealousy, not truly colored ideas of imagination, delight, and poetry. As such "green ideas," they are emotions, emotions of negativity which can but be furious in their fermenting and insidious attack upon the human heart. And, so, they "sleep" only in the sense that they lie in wait for their furious outbreak in the heat of an envious or jealous moment. They are akin to the phrase attributed to William Shakepeare, who wrote of the "green-eyed monster."
Such an imaginative phrase....my compliments.