Northanger Abbey is unique from Austen's other novels. Although it was published later, it was one of the first manuscripts that she wrote. The supernatural appears in Northanger Abbey because Austen is parodying the gothic genre, which was extremely popular in her day. She is poking fun at the supernatural and superstition and showing how seriously reading such novels can change a person's perception of reality. I would suggest her other novels do not include the supernatural because she is critiquing other aspects of society.
Including the supernatural in your story would definitely be interesting. If you are basing it off of Pride and Prejudice, the supernatural might seem out of place since it isn't present in the novel. However, that shouldn't stop your creative liberty if you think it would make an interesting story. Happy writing!