Will it fit?

For the case and cooler:

From the specs: "CPU cooler height: 155mm / 6.1 inch"
The cooler height is 158mm. Your call

I've found that the case dimensions are usually pretty conservative. My Antec One lists max cooler height at 155mm, but a 159mm CM Hyper 212 Plus fits with 3mm clearance, even discounting the side bulge.

It may or may not fit.