I don't think so. the level of expressed protein is not depedent of the time. it depend of the promotor and the condition of cell culture. the protein belongs to early or late categories because of the capacity of gene activation. for example one gene is under promotor who need activators who are rapidly present and permit to transcript early gene and the late genes need other activators who are present after. that's the principle of the temporally expression of the gene. perhaps you could search about phage or virus who use this way of expression. there is article on it.