Sadly we can't remove the icon yet without disabling Notification Center entirely.
Should you want to proceed, this procedure requires a short disclaimer.
This involves hacking your System folder; make appropriate backups and proceed with caution!
/System/Library/CoreServices and select
Notification Center.app. Press ⌘I to Get Info. Click the Lock icon at the bottom of the screen to unlock the settings (you will be prompted for your password). In the Sharing and Permissions portion of the pane, click the plus sign. Add your account as a special user, then set the Privilege column to Read & Write for yourself. Then, in the Name and Extension field, add the letter
x to the beginning of the file name, dismissing any warnings the system throws your way.
Reboot the system.
If you don't want to reboot you can use Terminal.app, which can be found under
killall NotificationCenter and press enter. This terminates the NotificationCenter process.
Note that this eliminates the icon, but also all Notification Center functionality.