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.
One common theme is self - discovery. Since Zenitsu has a complex personality, many fanfics focus on him finding out more about himself, his powers, and his place in the world. Another theme is friendship. He often forms strong bonds with other characters in fanfics, like Tanjiro and Inosuke.
One common theme is protection. Since Nezuko is a demon and Zenitsu is a demon slayer, there are often stories about Zenitsu vowing to protect Nezuko from other demon slayers or more dangerous demons. Another theme is friendship. They develop a unique bond in the original story, and fanfics often explore that further, like how they support each other through tough times. And of course, there can be a bit of a romantic undertone in some fanfics as well.
Typically, tanjirou x zenitsu fanfic often focuses on their strong friendship. It might show how Tanjirou's calmness balances Zenitsu's more excitable nature. Also, their shared experiences in the demon - slaying world are a big part of these fics. For example, they might face a powerful demon together and their bond is strengthened through the ordeal.