The case won't damage the iPhone battery. What it will do is prolong the internal battery because it's not going through as many cycles as you would with the external case.
My opinion on the case itself is that it's the worst looking battery case out there what with the strange hump; I'm comparing to the most popular cases such as mophie here. It's also silicone which sort of has me scratching my head.
With those two cons out of the way, it's certainly nice to be able to charge the case itself with a lightning cable. Afaik it's the only case out there that doesn't use USB.
Functionally, its the best by far for the exact reasons mentioned by the previous poster.
However, it does leave something to be desired visually, and while it makes the phone incredibly easy to hold in the hand, its a huge pain in the ass to pull in and out of pockets, especially jeans. The integration with iOS is fantastic, and the fact it trickle charges the battery should, in theory, prolong its life by reducing the cycles it goes through. This is heavily contentious mind you, but I'd like to think that Apple spent at least a few hundred man hours testing the most efficient way to implement this case before going to factory, which is why I trust that this won't damage the phone battery at all.
The trade offs, for me at least, are significant enough that after owning one since its launch, I've now decided to sell it on and buy a mophie juice pack wireless, as the wireless charging capability removes the need to ever use micro usb to charge the case and phone, which was my biggest gripe with third party cases.