No. Once a Story is scheduled, it keeps the design exactly as it was at the moment you scheduled it. Going back into the editor afterwards and changing that design — swapping a link, editing text, replacing an image — does not touch any Story that's already queued.
If you edit a design that already has scheduled Stories attached to it, those Stories stay on the old version. A link sticker keeps pointing at the old URL, and any text or image change you make in the editor won't show up in what actually posts. Nothing updates automatically, and there's no notice that a scheduled Story is now out of sync with the design you're looking at.
There's no "push my edit to the schedule" option today. To get the new version out instead of the old one:
The snapshot rule only affects Stories that were scheduled before your edit. If you create a brand-new schedule from the design after editing it, that new schedule picks up the latest version — it's only the ones already queued that are stuck on the old one.
Reels behave the same way: a scheduled Reel keeps the video it was scheduled with. Its caption, date and some of its options can still be changed, see Can I Edit A Scheduled Reel?
For the scheduling flow in general, see How Scheduling Works In Storrito.