Yes, I've been thinking about this for a long time. I first had ideas about this about ten years ago and it never became enough of a priority to push aside other MYOG projects.
Do you have a link to any information about Joe Valesko's hat? I was aware of it, but I wasn't able to find anything when I last looked.
I think materials could be identified that would serve all of the purposes one could dream up for a hat like this. I have some 30D aluminized silnylon that is shiny on one side and green on the other, for example. With this material, the hat would be waterproof, provide complete shade, would be aesthetically inoffensive (green side out), and it would be lightweight. With a drawstring around the perimeter and a kite surfing valve at the peak it could easily be used as a water bag or a stuff sack (or even a pump sack for a sleeping pad, maybe).
The problem, as you said, is keeping it hat shaped and secured to one's head in hat mode. If it were made of foam (like Joe's?), it would be simpler to solve that problem because the material might be rigid enough on its own. But a fabric one would have to be built like a kite, with rods, hoops, etc.
Maybe fabric with a foam insert? Straight foam would work as a hat, but I'm not sure it would work as a water bag/stuff sack unless it also had a layer of fabric.