As far as I can tell, the new elite controller does NOT allow for customization of the thumbstick sensitivity curves like the 2015 GamesCom video from Microsoft showed at 32m31s.
I hope I am wrong about this, but the Gamescom video showed the manual adjustment of curve points. The app in its current state shown in Fizzor's review of the controller and on Microsoft's accessory support page show 4 preset options only with no manual curve customization. You can choose from Default, slow start, fast start, and instant.
I hope someone has some insight into this issue, and hopefully Microsoft will fix this false promise soon since this is one of the main reasons I preordered this controller.
Microsoft's Gamescom video:
Microsoft's elite controller support page: