Hey Watchmaker!
What a fast response! I know the game will not magically look better, that is not the intention of a new API. The intention is to make the game run smoother, just like Mantle is doing (AMD Low Level API). I think there is a lot of improvement possible when it comes to performance for Guns of Icarus, especially when Guns of Icarus goes Adventure Mode (MMO, with huge maps perhaps and lots of things going on?) Also if Adventure Mode is going to have some persistence, I think drawcalls can fastly increase. (Depends on your plans ofc.)
Drawcalls are simply the things which can happen at a time. Here is an article about it on the Unity forums.
http://forum.unity3d.com/threads/what-are-draw-calls.27416/ The drawcalls possible in DX11/12 vs DX9 are way higher. So it means there are more possibilites for Guns of Icarus.
Hope this helps! Hope you guys will perhaps look into Mantle/DX12 aswell since those are low level API's which will improve performance very significantly. Mantle is not yet intergrated into Unity (and probably never will), so I think DX12 is the way to go since it will probably come in time to Unity 5.
PS: Amazing work on the DX11, cant wait to see it intergrated into the game!
Especially in hectic situations my performance tends to drop, not sure if this has to do with the drawcalls, but it could be.