[eluser]WanWizard[/eluser]
No.
Technically, it's not the session that expires, it's the session cookie that holds the ID of the session. When the cookie expires, the browser deletes it. Next request, the application doesn't see the cookie, so it creates a new session. The old record is still there, but it can't be associated with the user anymore.
You could solve that by not using the cookie expiration. Set the expiration so that the session never (or after your desired expiration time) expires. Then store your expiration timestamp in a session variable. On a page load, check this variable, if the session is expired, delete all fields related to a login (or destroy the session), and redirect with your message.