That's a great idea, but one of the many issues that you're going to have to work around is that you're going to want a model with detailed 3d textures for 3D printing, but most of the texture in games is from the 2D texture images.

The best solution you're probably going to get is to be able to save the pose of each part and then have to provide your own 3D models of each of the parts. At that point it wouldn't be hard to create a full 3D model of it.

To print it, of course, you're also going to have to divide it up into manageable sections that you can actually print.