I made the mistake of putting a quilt made with poly batting in the dryer at a laundromat. That dryer gets a lot hotter than the one I have at home, and so it melted the batting a little - gave it that "shrunken" look as if it had been cotton batting, and made it feel stiffer. Not enough damage to ruin it, but still I was upset.
I think you could iron a quilt with poly batting but your iron would have to be on a LOW setting, not cotton.