spellblade and prismatic burst supports and crown of eyes?

Lets say I am playing inquisitor with battle mage. My attack has both spellblade and prismatic burst socketed. Spellblade sems to support prismatic burst (icon appears on the skill).
1. Does Battlemage support prismatic burst?
2. Does crown of eye support increases to spelldamage of prismatic burst as attack damage for same skill?

1. Yes, it works for any spell that hits.
2. No, it’s a spell not an attack.

And most importantly:

3. Don’t do it. Prismatic burst has low damage, a long c/d and a tiny AoE. I don’t know what niche GGG thought this support would fill, but it’s utter garbage and will result in an extremely slow character that can’t farm the gear it needs to get strong.