I've been using my black Note with a white battery door for a few weeks now. I prefer this particular combination, mostly because I don't like white bezel around black screen. The deep blacks of amoled blend really well with the black bezel, in my opinion.
I ordered the white battery door through ebay and it feels like the actual samsung battery door for the white Note. It has the same stickers and same thickness/feel of the original dark battery door. One major difference is the white one is glossy, while the old black (dark blue?) one is textured.
If I managed to attach them, there should be some photos of the black Note with white back, on white and black backgrounds.