The displacement of the voxels can also be done with a simple matrix transformation, as far as I see it; same like you'd do for the nodes in a 3d model, same as you'd do it with a 'traditional' 3d pipeline (OpenGL/DirectX) - unless I'm behind the curve and animation itself is done on the GPU nowadays, but I don't think it is.
Ragged boundaries wouldn't be an issue as long as there are enough voxels. What I understand, that's the whole point - you just have lots and lots of voxels, at a much finer resolution than you'd ever want to render at, so that you just (by brute force) render once without having to worry about anti-aliasing, gaps between planes etc.
Yes, but the point is that you have to displace much more voxels than you'd have to displace vertices otherwise. Vertices are only on the boundaries of the object (and quite sparsely at that if you use normal mapping shaders etc wisely) but voxels fill the entire object densely...
I was under the impression that they fill the object's hull
With voxels, you'd have to recompute all the voxels of the object on a 3d grid. Also there are issues with ragged boundaries, which can be prevented by using antialiasing, but which is probably trickier (=more computationally intensive) than in 2D...