Sharing your visualizer to the Apple TV is Possible!
I have a mac book pro retina display 15"
Itunes 11.0.1
apple tv3
Go to display preferences
And set it to the following settings.
Then turn on your itunes
and turn on the visualizer
Then hit the spacebar to start the music it.
This should work hope this helps.
Also use the Itunes visualizer clasic it is less glitchy