Yes, automatically. A composed menu stores links to its source menus, not copies — every time it displays, names, prices, and descriptions are read live from the source. Edit a dish on the original menu (or change it in your POS) and every composed menu that links to it shows the new values immediately, with nothing to re-save.
Linked sections also track membership: add a dish to the source section and it appears on the composed menu; remove it and it disappears. Individually picked items track their own name, price, and description, but new dishes added to the source section are not picked up — only whole linked sections do that.
If a source disappears entirely — the menu is unpublished or deleted, or the item is removed from your POS — the composed menu skips that entry on the page, so diners never see an error or a stale price. In the composed editor the entry shows a warning flag instead. It is kept (not silently deleted) so the link heals itself if the source comes back; remove it in the editor if the change is permanent.
See Creating a Composed Menu for the full guide.
