It would have to, because it works that way for Sal and Zero. Execute and FFoH do 400% melee damage , along with roid damage. I don’t whether they multiply though.
Also, I would suggest taking unstoppable force. Gaige is slow, and you need to hit enemies to get that life leech, unless you plan on keeping discord on 24/7 or keeping a gun on hand for the skill that regens health on full mag.