You'll have to make each frame of the animation it's own "screen" in the texture. So instead of having one image for each different logo on the screen, you'd have an image for each frame of the animation in your texture.
If you want it to be a bit more "screen-like" you could also add a bit of a bump map that gives the impression of the 'screen door' effect, and don't forget to make the surface emissive in the config file!
On another forum (forget where) I saw someone do exactly that to great effect. I'll be doing the same when I get around to adding jumbotrons to my circuit, too.
Okay after playing around it for hour or so.
I am getting some where...I think
I created horizontal texture with T and T apart than every 256 pixels horizontally letter will be added between.
I still haven't calculated the pixel calculation correctly. And animation is too fast.
Maybe Ilja will add better solution later on.
It seems super tedious to make one simple add.