I could not say that as I don not have the dimension from the top of CPU to inside edge of side panel. In addition, w/o knowing the MoBo, this determination can not be made. That's a 120mm fan in the rear ... seems from the pic, a 150mm wide cooler will be a tight fit, especially with a Mobo that puts the GFX card in the 1st two case slots.
http://www.corsair.com/en-us/vengeance-c70-mid-tower-gaming-case-gunmetal-black
The Corsair C70 is 9.13 inches wide (232mm) and fits a 170mm tall cooler according to Corsair web site ... in other words, 62mm short of case width., Given the above, 8.66" (220mm) dimension you gave, taking off that same 62mm leaves us with ONLY 158mm to fit the 165mm tall cooler.
It's therefore a given that if...