Banshee's Sound Menu extension is specifically for Ubuntu's sound menu.
Banshee doesn't currently make use of the playback controls in Gnome Shell's message tray and notifications. That feature is Bug 645628 if you're interested in following the progress.
However, as Gamx points out below, even if this isn't possible out-of-the-box with Banshee, there are third-party solutions.
Webupd8's PPA provides a
gnome-shell-extensions-mediaplayer extension that allows you to control various media players -- including Banshee -- using the controls in Gnome Shell. To learn more about Personal Package Archives, see this question on Ask Ubuntu. To install the Gnome-shell extension, in terminal type:
sudo add-apt-repository ppa:webupd8team/gnome3
sudo apt-get update
sudo apt-get install gnome-shell-extensions-mediaplayer