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.
In the manga, Zenitsu and Nezuko have an interesting interaction. Zenitsu is charmed by Nezuko's cuteness and tries to protect her. Their relationship adds a lighthearted element to the story.
Definitely not. The story doesn't depict Zenitsu and Nezuko as a couple. Their paths in the manga are more about their individual quests and battles against evil.