Well... I'm not a music "expert", but I do have a degree in literature and some grounding in the basics of composition.
I think I'd say that the crossover is there... but it's so abstract and high level that it only really comes into play if you've also mastered all the stuff specific to those fields too, which is a huge amount to learn and may consume all a person's time and energy.
So like a story, a piece of music should:
Establish theme and tone, take the audience through a journey that keeps weaving in those themes, and set up and then satisfyingly tie off different elements to create a satisfying emotional experience.
The problem is, what the elements are is totally different. On an abstract level, yes, a character and a leitmotif serve the same purpose, but on a practical level, learning to write a character and learning to write a leitmotif are totally different skills. My knowledge of literary structure may help me plan the general vibe of a piece of music, and the different moods I want it to move through... but it won't magically help me know time signatures, or choose what mode to use for my chord progressions, or give me insight into the range of different instruments or how to construct a rhythm.
Or in reverse, knowing how to write a symphony will probably help a composer to plan out the overall journey of a story, and the feelings they want it to move through, but won't magically let them know whether to write in 3rd or 1st person, how to use language effectively, write a natural feeling conversation, or similar skills specific to writing.
Really, when we're talking at such high level, any skill could potentially enhance other skills. For example, I know that the discipline of classical musicians and the care they take as well as their excellent hand-eye coordination often makes them good artists, but then, engineers often make great artists and composers too due to their attention to detail and consistent sense of structure. Comedians often make good musical performers and vice versa because of their sense of timing and strong emotional expression and improv skills. So if you want to be a good writer, learning almost any skills outside of writing may improve your writing so long as you also keep working on learning writing skills and gaining experience in writing too.