I've just installed 13.10 and while I was using Firefox, the system prompted me to install the webapps for sites like Gmail, Facebook, Launchpad, and so on.
What happens is that, after the first moment of the installation, the Unity icon that appear for Gmail app remains as only an icon that opens another window directly into Gmail. Before, there was an integration with Unity because when clicking the icon it directed me to the tab where Gmail was opened in Firefox.
Besides the Unity integration there's the message menu integration. With Facebook app, I receive notifications on the Me Menu near the watch whenever someone sends a message, but with Gmail it's null, it doesn't even appear in the Me Menu. It happens with Firefox and Chrome.