Offline Mail is not supported by your browser
Is it really the case? Or is there something I can do to be able to use Gmail Offline?
Actually Gmail Offline is migrating from Gears to HTML5 so it's not working these days. You have to wait until Chrome12 to get the new updated Offline Service.
Offline GMail uses Google Gears which isn't available for Mozilla Firefox 4+, Internet Explorer 9+, and Google Chrome on Mac or Linux.
See the complete system requirements here
Offline Gmail is now available for Ubuntu as an app through the Chrome Web Store: https://chrome.google.com/webstore/detail/ejidjjhkpiempkbhmpbfngldlkglhimk
(tested on Ubuntu 10.04, Chrome 13)