Plywood layers are ran in alternating directions to increase stiffness. Rip ya a 3/8 square about 36 inches long and whip it in the air, probably break off near your hand.
Laminated arrows are ran in the same direction. Im sure you could make an arra, but the spine would probably be heck to get consistent,not to mention the voids in the plywood layers. Even the 5x5 Russian birch plywood with the extra layers used for cabinet drawers and such have voids here and there.>>>>-------> Not sayin dont try, I've just been thinkin about various woods and methods also.