I may make some enemies here, but try it out! give the boy a pillow.. a big one, even... If you are considering not d/t the risk of SIDS, think about the fact that your son is an able-bodied toddler. He is mature enough to be able to re-position himself if there is any danger.
Common sense says that a 15 month old is far more stable physiologically than, say, a 15-day old.
By the way, my son sleeps with a boppy. I lay a duvet over it and it creates a little nest for him. He used to sleep on his tummy with the pillow under his chest/ armpit area, but now he likes to lay on his back with the "arch" of the boppy under his neck.
The fact of the matter is that there are correlative links between SIDS and blankets/ pillows/ back-sleeping/ male sex/ smoking in the home/ prematurity, but there are also cases where none of these factors were in play.
Good luck, and use your best judgement.
J.