Am am unsure if this changes the value of subject of the Berserking Enchant but if you read
Armored to the Teeth - Spell - World of Warcraft it says the spell only ticks and applies itself every 30 seconds. Thus, depending when the enchant procs, you may or may not receive a reduction in AP from AttT.
Along with that, depending on when that 'tick' happens, you could also lose that armor for 30 seconds while AttT refreshes to see if your armor value changed again. You might not even have the AP from the enchant proc at that point in time.
If that is in fact how AttT works, Berserking seems like a potentially risky enchant.