I'm not sure if any browser available currently support this, but I
suppose none. Maybe if it became RFC, you might get Mozilla folks
interested with this :)
As far as I know, Mozilla guys are hanging out for TLS/SNI, as is the
rest of the world. They and the other browsers have been ready for
ages. There was a big push around 2005-2006 to get over to full TLS
because of SSLv2 bug and the emergence of phishing as an MITM.
TLS/SNI is the "real fix" for the bug, whereas other tricks (and there
are quite a few of them) are all suspect for one reason or another;
when you try them you discover what goes wrong. There's a list of
possibilities here:
http://wiki.cacert.org/wiki/VhostTaskForce
http://en.wikipedia.org/wiki/Server_Name_Indication
TLS/SNI is working in Apache httpd, and has been for a while, but is
unreleased. I don't know or understand the reason for that.
iang