Rather less... To cool the processor properly in all situations, I would either use a powerful air cooler or a 280/360 Wakü:
Air:
Noctua NH-D15 (16.50cm)
be quiet! Dark Rock Pro 4 (16.28cm)
Water:
280:
Corsair H115i Pro
NZXT Kraken x62 incl. AM4 (3cm)
360:
Corsair H150i Pro
NZXT Kraken X72
On the Corsair website it is shown mounted on a Corsair Spec Alpha case.
Here is the link: http://www.corsair.com/fr-fr/landing/specalpha
You have to scroll down to the bottom of the page, click on a picture and scroll down
Since I've been on the H100i v2 version, since I changed the box and could take the other one. However, from the looks of it, it wasn't noisy. Even the one I have now, when I use four fans on it (top/bottom). If the fans are too noisy for your taste, you can always get another one. As far as the pump is concerned, I can compare it with the one I have now (it's roughly the same, just a bigger radiator) and I must admit that I don't know if it's the fans or the pump that's running. That's how stealthy it is. (The fans are at about 500 rpm, as you seem to know a lot about them, you understand that this is the minimum, and therefore very little noise.
Yes, according to Aquatuning, this should have space.
http://www.aquatuning.de/download/Gehaeuse-Radiator-Kompatibilitaetsliste.pdf
(Without guarantee - However, this is the only specification I could find)