UVs definitely play a roll in mudbox. They are required for texture mapping. You can layout your uv in 3dsmax by hand which is generally better, or you can let mudbox automatically generate the uvs for you. There is a difference between manually unwrapped uvs and automatically generated uvs. Auto UVs break up ever quad polygon into its own uv island and projects them and arranges them into each uv tile. This makes it hard to edit in photoshop if you need to do any fine detialing.
Photoshop is always good to have and use when texturing, but Mudbox 2012 is a very good texture painting program. You can import images and project and paint them directly on to your model in layers, and evne use laayer masks just like in photoshop.
You can even export your layers as psd and paint them in photoshop, and reimport them back into mudbox seemlessly, without losing your layers in mudbox or photoshop. This can be quite useful.
Anyways, UVs are required, because mudbox's greatest strengths is that it can paint multiple uv tiles interactively, but of course your model needs uv coordinate to be able to paint it. UV tiles if you're not aware, are regions within the uv cordinate system. If you notice there is a 2d grid in your uv editor. U represending X, and V, Y on the grid, you can break up those grids into tiles. This is good for memory management. Mudbox is designed to paint images on different uv tiles, so that it can maximize memory effeciently and use as much pixel data as possible per tile.