I’ve never embedded an app in an iframe, so I can only speculate.
I’d expect not, though it depends on how you’ve embedded the app. I’d expect unsynced changes to be saved in the browser until the embedded app is opened again, at which point I’d expect the sync to resume. This would be very easy for you to test. Very, very easy. Trivial, even. Have you tried?
When an AppSheet app is embedded in an iframe, syncing is handled entirely within the browser session. If the user closes the page before the sync finishes, the pending changes are discarded because the local app state is lost, and AppSheet will not retry later without that session. To avoid data loss, you can enable Delayed Sync or Automatic Sync in the app settings so submissions are pushed immediately before the user navigates away, and design forms to save data on each change rather than only at the end. You can also consider breaking longer workflows into smaller saved steps so each commit happens before the user exits.