I doubt it, but some prominent Rusty guy seemed to indicate this must be so.
4:00 am on Nov 20, 2012 (gmt 0)
If you aren't running HTTPS on a web server the port 443 would probably not even be running and the server will reject a connection on that port.
Using Firefox to browse to a site using https that doesn't support it gets you an error message "Firefox can't establish a connection to the server at example.com" You get similarly non-specific errors in other browsers.
Trying to give a friendly response you would probably actually have to server up a HTTPS site with the message, otherwise you will hit all sort of security issues as the browser will either think you are trying to server insecure contents on what should be secure connection or that there is some malicious man in the middle attack happening during the handshake.
10:29 am on Nov 20, 2012 (gmt 0)
so what happens if you are correctly running HTTPS and all the pages on a site are correctly indexed as HTTPS?
Does "not provided" somehow disappear?
Does Google Analytics no longer strip the referrer?