If marriage is redefined to mean "any permanent relationship," will mating couples be less likely to marry?

Judicial decisions in several states have redefined marriage to include non-mating couples, implying a new definition of marriage as any permanent relationship. My question is how this redefinition will affect actual mating couples who have the choices of hooking up, cohabitation, and marriage. Will they be more likely, less likely, or equally likely to marry if marriage means any relationship?