No, I wouldnt have thought a H100 would work.
If youre ok with Air cooling, then your case should be fine as long it fits your upgrades in it (which it should).
If you do get a third party CPU cooler like the 212 Evo - Id highly suggest Overclocking your CPU up from 3.3ghz - itll make a huge difference.
I have the same CPU but OC'd to 4.6ghz and the difference in performance is definitely substantial, increasing FPS in games like Skyrim by up to 15.
In fact, when my OC got reset after some BIOS updates, which I didnt immediately notice, after I started up a game I instantly thought 'wtf.. why am I running slow' haha