Definitely not. In the manga, there's no such plotline of Zenitsu and Nezuko getting married. Their relationship is more focused on being comrades in the fight against demons rather than a romantic one leading to marriage.
Well, in 'kimetsu no yaiba the first novel', it probably focuses on the early days of the main characters. It could be about Tanjiro's journey as he first discovers the existence of demons and decides to become a demon slayer. It might also include his encounters with other important characters like Nezuko, and how their relationship develops in this different narrative format.