Growl does not pass on Tweets to Notification Center
While creating this question, I figured it out.

Twitter was not yet listed in the Growl preferences as an app that was outputting to Growl. Simply restarting the Twitter app fixed this. Oddly enough this wasn't necessary for Adium or Colloquy.



Works fine now! Channeling the notifications to Notification Center strips them of profile images and the Twitter program icon, so I'm sticking to Growl's defaults.