When a user tries to access for example a bookmarked page such as "unread content" (which some of our users have set to as their browser's default page), if the user is not logged in, they see this negative statement, rather uninviting message. Couldn't they see a Sign in form instead, with a positive message inviting them to sign in such as "to view this stream, please sign in"? 

Not exactly what you’re asking but this will add a Sign Up link in the error messages, just in case the guest hasn’t an account to sign in.