While they didn't build battleships out of Pykrete they did build fuel tanks out of laminated paper and plastic. (An early form of fibre glass, using paper instead of glass.)
(http://www.ww2aircraft.net/forum/other-mechanical-systems-te...)
(http://www.ww2aircraft.net/forum/other-mechanical-systems-te...)
In general, paper based phenolics were used for tons of things, and if you have anything around that looks like hard plastic that was made before the 70s you've probably encountered it as well (buttons, knobs, etc...). The trade name Bakelite was a general term to denote a paper/linen/cotton based thermoplastics.