The answer is yes and no. Yes for most up to date browsers but no to some old ones. Unfortunelty since this is a newer technology the error messages for this issue on older browsers is less than informative. It is down right scary. It says;
There is a problem with this website's security certificate.
The security certificate presented by this website was issued for a
different website's address.
Security certificate problems may indicate an attempt to fool you or
intercept any data you send to the server.
We recommend that you close this webpage and do not continue to this
Click here to close this webpage.
Continue to this website (not recommended).
If you arrived at this page by clicking a link, check the website address
in the address bar to be sure that it is the address you were expecting.
When going to a website with an address such as https://example.com, try
adding the 'www' to the address, https://www.example.com.
If you choose to ignore this error and continue, do not enter private
information into the website.
SSL support with SNI on shared IP addresses requires that the user's browser supports SNI. Most modern web browsers support it (e.g., IE 7, Firefox 2.0, Opera 8.0, and Chrome). However, there are a few outlier exceptions:
- Any Internet Explorer browser on Windows XP
- Chrome 5 and older on Windows XP
- Blackberry web browser
- Windows Mobile phones up to version 6.5
- Android mobile phone default browser on Android OS 2.x
Browsers with support for TLS server name indication
- Internet Explorer 7 or later, on Windows Vista or higher. Does not work on Windows XP, even Internet Explorer 8.
- Mozilla Firefox 2.0 or later
- Opera 8.0 or later (the TLS 1.1 protocol must be enabled)
- Opera Mobile at least version 10.1 beta on Android
- Google Chrome (Vista or higher. XP on Chrome 6 or newer. OS X 10.5.7 or higher on Chrome 5.0.342.1 or newer)
- Safari 3.0 or later (Mac OS X 10.5.6 or higher and Windows Vista or higher)
- Konqueror/KDE 4.7 or later 
- MobileSafari in Apple iOS 4.0 or later
- Android default browser on Honeycomb (v3.x) or newer
- Windows Phone 7
- MicroB on Maemo
To learn more about SNI and client software that supports it, refer to http://en.wikipedia.org/wiki/Server_Name_Indication.