I doubt it. EBSoH hasn't triggered on armour ignoring damage in the past and I doubt it'll trigger on it now, much less on Life Steal.
It's really easy to test too.
You can equip an elite necro skill on any other class. Just go to the master of dmg and see what it does compared to what the skill description says it will do. But no, EBSoH does not effect life steal.
I have a question while we're at it. Will heroes use Ravenous Gaze on the mobs? Half of the time with the elite skills, I feel as if I'm the only one using them.