Ok, sent staff to the Apple store and got two cases, here's the data -
Standard Apple silicone case: 9.5 mm thick
Smart Battery Case from Apple: 11.5 mm thick (at thinnest flange). Wow!
So even the flange area is way too thick to fit in the NanoStand XL without modification.
The Center of Gravity was not an issue for the 6s and smart case though.
So if you want to use the battery case in the NanoStand, you'll need to trim off a couple of mm of polycarbonate at the NanoStand's contact points.
BTW - we have a lot of different iPhones here. Looking at the smart case, which is only available for the 6, that combination seemed to us to be more bulky overall than the 6plus. The backpack + thick case sort of kills the compactness that we think is so nice about the smaller 6.
And the 6 plus already has almost twice the battery, built-in.
So for the same 99 bucks extra, you get both a big battery and big screen if you trade up to the 6 plus. Just another way to look at it.