Adding a character or adding traits to a character that don’t fit into your plot makes writing a good story more difficult.
The traits of your character are important elements in making the story come to life. If the traits are superficial or treated facilely then the they’ll standout as superficial.
Research is always the best place to start. Its important that those traits either impact the plot or serve to showcase the character’s inner struggle or reflect some element of their personality. It doesn’t matter if that trait is that they are married, blonde, redhead, or suffers from mental illness.
The plot can revolve around the trait, but that isn’t all a necessity. I think it depends on the intensity of the trait. For instance, if a character suffered from untreated paranoia, or pronoia for that matter, it should impact the plot since its a very severe condition. Imagine a romance involving a paranoiac that was never complicated by the character’s traits. I wouldn’t think it would feel genuine.