When entering archon form while wearing CoE, do I need to trigger it as the CoE is in the archon part of the cycle to get max dmg, or does the elemental dmg bonus change as the ring cycles even in archon form?
Gain 150–200% increased damage to a single element for 4 seconds. This effect rotates through the elements available to your class in the following order: Arcane, Cold, Fire, Holy, Lightning, Physical, Poison.
Equip it and see as it begins to rotate through all four elements. It doesn't need to be triggered. As long as you have it equiped, you gain the 150-200% damage increase to one element. Check your buff bar. It does this even in Archon form.
Even if you use only one element (let's say fire), it still gives you a 50% damage increase.