No, it doesn't work this way.
You can use the identification API to tell Sitecore: the current user is this contact. You would normally use this API when the user logs in.
Once you implement this, the users will log in and thus identify themselves to xDB.
Now, the user can log in to your site from multiple devices, or in several browsers on the same machine. Later on, even if he's not logged in anymore, xDB will still remember the last associated contact using a custom cookie.
If the user opens browser sessions from two or more devices, all simultaneous user sessions will have a common, shared, session. What this allows you to do is modify the contact in one session and access that changed state in another session simultaneously.
So there is no magical way for Sitecore to know who the user is if there are no identifying cookies in his browser, or e.g. a custom URL argument containing a contact ID. Shared session is about sharing state between multiple parallel sessions. Read more here: