I tested this and my initial observation was that it doesn't.
However, I only used the starting destruction spell flames as I didnt want to progress too far before finding out my Orc Mage was not viable. Using flames made it difficult to see if a 2x bonus was occurring.
Am I correct in assuming the berserker ability does not affect spells?
Best Answer
The strategy guide confirms that it does not affect spells (emphasis mine):
Melee combat consisting of one-handed and two-handed weapons, not spells or bows.