You can move the itunes library to the TC.. use the normal apple instructions for moving the library.
How to move your iTunes library to a new computer - Apple Support
BUT.. 2. You cannot stream from the TC.. the TC is a dumb as a board hard disk in a router. No media extensions.. no clue whatsoever.
So this makes it just one more item in the network to slow you down.
You still need a computer running iTunes.. to stream to apple TV. And this is a problem because if you use wireless it will try to stream in both directions..
TC--Computer.. Computer--TC.. TC.. ATV. And that is unlikely to work very well.
So at least the link to the computer should be ethernet.