No, and as a matter of fact there is very little evidence for Theseus as a mythological figure until the sixth century or so, when he begins to appear on pottery scenes. Theseus was a bit of a "fake hero" whose importance and mythology was largely a product of the Peisistratid era of Athenian history, when the titular tyrants were creating and recasting a whole variety of different cultural institutions (including, in fact, the centrality of Athena) in order to emphasize a unified "Attic" identity. Gantz goes into this in Greek Mythology.