I am not sure it can actually be done legally. I don't have any friends at the DMV, (which I find odd, considering how much time I spend there) who could help in the hypothetical discussion. However, if you can register an identical car under "Special Constructions" regulations, I would see some precedence for resurrecting a rusted out (not totalled) chassis.
It's a great question. I hope someone with more experience can offer some insight.
Also, I don't know for sure that it would not meet the specs. The final construction would be the same as the original design, becasue the rear frame rails, bub frame, doors, hood, fenders, et al, should be original design, right?