will the CPU cooler fit ?

Go look at the specs of the cooler (mainly its height inc fan) and compare to what Corsair says the C70 can fit as a maximum cooler height.

Its not hard to find out yourself.
 
No idea what the CPU clearance is. I've read 158mm and also seen 18.8cm and Corsair does not seem to think it's important to give that measurement. A mate had a PH-TC14PE in his for awhile.

A good rule of thumb is most cases with 120mm back exhaust fan can fit 160mm coolers, but that not always true.
 
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