If you want to do any sort of custom drawing or animation you basically can't do it with the web, the performance just isn't there. You must stay on the specific fast paths offered by the browser or you're screwed.
So no, the web cannot do pretty much anything with content and data. The web can do very, very little with content & data, it is just often enough coverage for passive things like articles.
I don't know what kind of custom drawing you are referring to.. the web can work with 2d and 3d drawing and animations just fine. For example, an entire first person 3d game built using WebGL - http://www.littleworkshop.fr/keepout.html.
So no, the web cannot do pretty much anything with content and data. The web can do very, very little with content & data, it is just often enough coverage for passive things like articles.