[67ChevyRedneck]

You could weld the cut portion of the door to the cab so it "looks stock" but then you run into the problem of the window being inside of the old upper door frame, so the door won't open/close without rolling the window down first. It would be a cool mod, but there would be a few issues to overcome, like I mentioned above, or what yukon jack mentioned with a huge cab/window frame gap.

I'm sure it's been done before, or something similar has been done, but the closest I have seen done to what you're describing is a truck with the top cut off.