Cgpt may already be "trained", even if less directly, by passages from fictional books. It is why unintentional breech of copyright can be an issue. You can prompt it even outright to mimic the style of an author, with mixed results.
I think it can be interesting to try to come up with a general plot of how it strings sentences together, although it will be only a subjective idol to form - after all, if one was serious about rigorousness there, they can just read the accompanying data about how cgpt works.
While a cgpt (or similar) fiction piece can be helped by the very ambiguous nature of literature in regards to what the author calculates in the text and how the text is actually picked up by the reader (even the same reader will see different things in time), my sense is that for any "ai" fictional story to be of some interest you will need copious amounts of work by the human who directs it with prompts and other refining processes, which is why I do feel that currently you are better off writing everything yourself from the start.
All that doesn't mean one can't find fun in using ai for writing; anything can be interesting, if you have the intelligence and will to extract from it. After all, you are reacting to a new text, which is bound to allow for some useful reflections ^^