The novel, as the title suggests, was left unfinished due to Fitzgerald's struggles with alcoholism and health issues. He only managed to complete about half of it before his death in 1940.
To answer your question, Fitzgerald's "The Unfinished Novel" was indeed unfinished.
However, it's important to note that "Edwin Drood" is also the title of a novel by Charles Dickens, which was left unfinished at his death in 1870.
So, there are two unfinished novels, both with the protagonist "Edwin Drood," but written by different authors.