I think it’s best to test it and see.
With one of my old stories, I deleted all of the characters and removed the scripts etc but I didn’t press publish again, all I did was save those changes, so everything was still live on the app (the way it was before) even tho I had deleted pretty much all of its content in the portal, but if I had pressed publish again, it would’ve been blank. I never deleted any of the backgrounds from the catalog though, so I’m not sure if it would also apply to your backgrounds and overlays. It could, I guess? But if you revisit your script and save, you’re definitely going to get an error saying they don’t exist if you’ve deleted them.
I already asked this question in this closed thread:
The responses said that it will absolutely delete it in your story and it’ll be a blank or dark screen, especially when it’s published. You can support the feature to add folders in the portal so every background and overlay isn’t crammed all together for all stories: