Must a page be published in order to be added to menu?

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The page must be published, as detailed in the “Adding Items to a Menu” section of the WordPress Codex WordPress Menu User Guide:

You can add different link types into your menu, these are split between panes left of the menu you’re currently editing.

  1. Locate the pane entitled Pages.
  2. Within this pane, select the View All link to bring up a list of all the currently published Pages on your site.
  3. …

Follow the link to see the rest of the steps if you need full instructions for adding a page to your menu.