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can bump do this? a low poly model that has a sharp mesh? and then make it more round and smooth? 

I didn't notice this question earlier, but no, a bump map can't make the geometry more round or smooth, but then again neither can a normal map.
All the biggie 3D apps (far as I know) allow for subdividing geometry at render time and/or in OpenGL (or DirectX) display to customizable levels. That's probably where that figure gets the smoothing look, although some programs such as Maya allow for actual normal smoothing, which isn't the same as surface smoothing or subdividing.
The normal map is just icing on the cake, for the sake of detail.  A high res 32 bit displacement map over a highly subdivided object would look a lot better.

But I suspect you know all that and it's just a rhetorical question.