Yes it is affected by battle spirit. This set is also currently bugged. If you get cleansed by purge, mutagen etc.. you will lose the 5 piece bonus until you re-equip a piece of gear.
That being said this set is still useful for a mDK with a lightning staff. I heavy attacked my way through vMA with not to much trouble.
I have dropped about 2.5 mil AP on this set and haven't seen any rings yet =(. I got 4 necklaces though and lots of weapons. Rings should drop too right? does anyone know?