That is not how it works. Fire damage is just a type of damage, like Cold damage, and the Stygian take additional effect against Cold, and some demons are 'immune to fire' thus are immune to fire damage. So those fire based arrows wont effect the demon, and if they were cold they would have an added effect on stygian. So no, you cant damage Risen with those fire arrows, unless players 'agree' to, but that is not how it works with the rules as written.