Sure. It will work with your exact gear, but would be better with more attack speed.
you already have an apoc Trium, which is fine, but I would go with a meteor, vit Oculus http://us.battle.net/d3/en/item/the-oculus
It is the free-est -meteor thinggy you will get, since it also has apoc, damage and high crit natively, it is a humdinger of a bargain.
You could use an SOJ in place of the unity, I tend to use my rare ring even though I have an SOJ though, because crit and attack speed are actually probably more important than -cost.
Casting 2 spells with animations, you will find yourself wishing for more attack speed, that is for sure, and the lack of apoc on your sword will be a much smaller deal than the lack of speed. Stick with life steal, it is not optional. you are plenty tough as far as mitigation goes.