Oh yes, very much so. One of the best examples is the ancient Greek comic playwright Aristophanes who was both famous and infamous for his parodies and caricatures of the living, dead, and divine.

For instance in his play The Frogs he has a wimpy Dionysius try to bring the recently deceased poet Euripidies back from the dead because all of the current tragic poets suck. Later in the play comes a poetry slam between Euripides and the poet Aeschylus where each parody each other and each other's work.

Other plays go even further into parody, humor never really changes.

Yes, absolutely. In addition to /u/wolfram184's comment on Greece, it happened in Rome. Marcus Tullius Cicero, the famous orator, in his Pro Caelio, a speech in defence of a man accused of trying to murder a woman named Clodia, made use of parody to great effect. The speech was essentially a series of ad hominems directed at Clodia, villainizing her to make Caelio seem morally upright. At one point, he starts impersonating Appius Clodius, the creator of the Appian Way and an ancestor of hers who was certainly well known at the time. He essentially scolds her in the persona of Appius, talking about how she's dishonoring the family and not behaving properly with her wild accusations against Caelio.