zealot's oath, life gained by attacks, ES

i have zealot's oath, i just noticed that it specifies "life REGENERATION is applied to energy shield instead". I'm using a claw and the question is, does life gained by attacks count as life regeneration? will it go to my energy shield instead of health?

Ignoring the fact that you could easily test this given a couple minutes, the Gain from the Life Gained on Hit is not the same as regeneration.

thanks for the answer! i'm new to the game and still unclear about certain concepts. so the life gained from the claw does not benefit me at all, that's clear now. what if I add ghost reaver on the tree? does life gained on hit count as life leech?

No, leech is a specific mechanic, separate from life gain on hit.
If I've got my facts straight, the only way to gain energy shield on hit is through items specifying "Energy Shield on hit", like a Watcher's Eye with "+# Energy Shield gained for each Enemy Hit while affected by Discipline".