For the surveys in Survey123, is it possible to set option for Everyone(Public) to submit the survey, but the survey itself can only be found when the survey link is given, just like the option when you give someone a publicly accessible link to edit a private Google Docs.
No, this is a limitation of the sharing capabilities of ArcGIS Online or Enterprise. When an item is shared as public, it is available to everyone via search, links browsing etc. It can not be public and hidden. If this is something you are wanting, I would suggest posting in the ArcGIS Online forum, or raising a support ticket with Esri Support for allowing public and hidden items in ArcGIS Online and Enterprise when managing sharing permissions.