Yes. For example, if you have a 5 power Monster, it will deal 1+1+1+1+1, all simultaneously. If you try dealing it to a warded unit, the Ward will prevent all of it. If your opponent has Shield Maidensnearby, each damage will be reduced. If you have Panpipes of Pnom, it will be 2+2+2+2+2 damage instead.
