I think you can do this with bones,
may be a bit hairy but....
spiral_still_1.19.jpg [ 12.75 KiB | Viewed 528 times ]
spiral_still_2.15.jpg [ 12.47 KiB | Viewed 528 times ]
You have to use the ADD mode to rotate the bones (all at once)
and you have to draw the bones first in a spiral shape (to set the initial rotation)
after you have drawn the initial shape you can straiten the bones one by one and when its flat envelope the plane to the bones, then its just a matter of using add mode...