In regard to the idea, I like how it sounds on paper. More variables in battle is usually a good thing, though I could see myself getting frustrated having to sometimes rely on luck to beat a battle. If I'm fighting a boss and it's almost dead and I only have one character standing, I'd be screaming at the other character through my computer/TV "wake up you lazy f*&$s!" If my standing character is KOed, I'd be pissed knowing that if I had been luckier and one of the others had woken up I could have won.
Actually, in BoF games, there is a stat called guts and in no.3 it's invisible. It doesn't work like normal stats do by increasing as you level up. I think it's fixed for each character or has to do with the number of fights you've been in. You could make such a stat with variables. You could also set this ability to work only if you have an item equipped or a status in place.