Are you generating the 3D mock up in PS with the 3D tools? It is pretty straightforward to do so - take your extended (mirrored) image and slice it with guides along the "fold" lines. This will divide the image into 9 images. It is then just a matter of assigning the proper images to the diffuse material of the proper faces of a cube - the cube should be resized to match the aspect ratio/dimensions of the wrap piece and the corresponding source image.
As far as automation goes, I have not fooled around with automating 3D in PS. If the sliced image sets are named uniformly and predictably, and you can assign the texture maps automatically through an action, then you should be able to automate the process in a scene that has the 3D model prepared and sized properly.
A shortcut might be to pre-render a generic 3D scene (with the background and drop shadow, etc.) and then take the appropriate slices and skew/warp them onto the faces of the pre-rendered canvas. This will save you render time, as the faces of the cube will have the shading baked into them and you can lay a copy of the baked shading on top of the skewed faces an set the blend mode to multiply.
Still, automating would need investigation, either way.
You may also be able to try it in one shot by adapting the UV coordinates of the cube to suit the mapping of the mirrored image so that you only have to apply the image once and the wrapping will be handled by the UV coordinates.
kirk