No. The Prieuré de Sion (Priory of Sion) was a fake secret society create by a French con-man named Pierre Plantard. Plantard created the Priory in the 1965 as part of an elaborate hoax to crown himself the rightful king of France. To pull it off, Plantard and his accomplices forged documents and placed them in the French National Museum. The fake documents were later used as the basis for the 1980s conspiracy book, Holy Blood, Holy Grail, which Dan Brown later used as the basis for The Da Vinci Code. The Priory of Sion as described by Brown, never existed. There was however, a 12th century monastic order founded by Godfrey of Bouillon called the Abbey of Our Lady of Mount Zion.
The three monkeys are Mizaru, covering his eyes, who sees no evil; Kikazaru, covering his ears, who hears no evil; and Iwazaru, covering his mouth, who speaks no evil. There are various meanings ascribed to the monkeys and the proverb including associations with being of good mind, speech and action.