Does signing a temporary (ʿurfī) marriage contract—without cohabitation or marital rights—as a joke, constitute an ʿurfī marriage?

Marriage is one of the great rites of Islam, and it has conditions and pillars without which it is not valid. Among the most important of these are the presence of a guardian and witnesses, along with an offer and acceptance that are not restricted by a specific term or the negation of cohabitation. The formula mentioned in the question is nothing more than mockery and play, and it is closer to the enjoyment marriage (Nikah al-Mut'ah) which is forbidden by Islamic law. As for customary marriage (Zawaj Urfi), some forms of it are valid if they fulfill the conditions, even if not documented in court, while others are invalid if they lack some of the pillars, or if they are merely an agreement between the young man and woman for marriage and cohabitation.