it does, at least for claw II which i was referring to. the [b]highest[/b] of the 3 principles fuels attack (so if you have just one them, you get 1/3 of its value added to attack), but the [b]lowest[/b] of the 3 fuels regeneration, which, in case you dont have all 3, will get zero. (i guess it doesnt matter for you since your regen stat is high enough to get all your creatures back to full VE anyway ) btw, i think when you have at least 2 of them, it should get 1/3 of the other principle, instead of zero, but that wasn't the case when i tested it yesterday.
i know that claw III (still) gets 1/3 of the highest / only principle to attack, power and initiative.