According to David Schneider and Adam Reich it does, their paper is called Marrying Ain’t Hard When You Got A Union Card? Labor Union Membership and First Marriage. The abstract is this:

Over the past five decades, marriage has changed dramatically, as young people began marrying later or never getting married at all. Scholars have shown how this decline is less a result of changing cultural definitions of marriage, and more a result of men’s changing access to social and economic prerequisites for marriage. Specifically, men’s current economic standing and men’s future economic security have been shown to affect their marriageability. Traditionally, labor unions provided economic standing and security to male workers. Yet during the same period that marriage has declined among young people, membership in labor unions has declined precipitously, particularly for men. In this article, we examine the relationship between union membership and first marriage and discuss the possible mechanisms by which union membership might lead to first marriage. We draw on longitudinal data from the National Longitudinal Survey of Youth-79 to estimate discrete time event-history models of first marriage entry and find that, controlling for many factors, union membership is positively and significantly associated with marriage. We show then that this relationship is largely explained by the increased income, regularity and stability of employment, and fringe benefits that come with union membership.

That is via the excellent Kevin Lewis, who cites some other interesting papers at the link.