We played that match twice - with Darkness and (just for fun) without it.
With Darkness, the Orc lost without a chance. Without Darkness, I lost, but the Phoenix wasn't defeated. They just tore my army apart. Strangely, I had a full Darkness skill, but not a full Summoning skill. I didn't have Walls or a Hive. Maybe if I had used walls, I could have won without Darkness...
Therefore, I stick to my opinion - Anti-Chaos and Anti-Summoning significantly reduce magic power. But Anti-Darkness doesn't have much of an effect.
Added 4 minutes later
A well-developed Warlock or Necromancer can have a Phoenix under Shield withstand an attack from hundreds of Black Dragons. The question is whether the Orcs can gather that many troops. ;)