Cooler dimensions: 116 x 51 x 159 mm (4.6 x 2.0 x 6.3 in) (From the coolermaster website)
Case clearance: 143.5mm (with fan) (From the NZXT website)
So no, doesn’t look good. Get a wider case or a smaller cooler.
The case's side panel doesn't have a fan hole or a fan installed.
For me, it's okay if the cooler just touches the side panel, but doesn't bend it.
Also, I didn't clearly specify the case model. It's an NZXT gamma classic series