Well... No. Genoese pesto, probably. Pesto in general, as in a sauce made from pounded/puréed herbs, nuts, oil, etc., no. This recipe appears in De Re Coquinaria, the first cookbook in existence.

[215] ANOTHER [SAUCE FOR] CRANE OR DUCKALITER IN GRUEM VEL ANATEM ELIXAM

PEPPER, LOVAGE, CUMIN, DRY CORIANDER, MINT, ORIGANY, PINE NUTS, DATES, BROTH, OIL, HONEY, MUSTARD AND WINE [1].