No — the editor autosaves a moment after every change and shows when anything is unsaved.
Publishing is separate: it freezes a snapshot as a new version, and that version is what your live link shows. Versions in the brand menu lets you view history and roll back.
Overlays started from a GridCast layout also get a GridCast updates button when we improve that layout. You choose which changes to take, your own edits are kept, and you can undo.