Whether it fits or not is kinda moot. It either fits or it doesn't. 1mm clearance is enough in most cases. However, some case sides are a real p.i.t.a to close and require some pressure in the center of the side to get all those stupid little tabs to enter their respective slots. In that case, you can say goodbye to that 1mm of clearance as the case side will flex inwards. It's also possible to use the heel of your palm just like an 'English wheel', from the inside of course, and actually flex the case side outwards, giving 2-3mm of clearance above the cooler.
'Iffyness' aside, the better option would be not to get the Hyper212, very good and very popular budget cooler btw, but to shop around for alternatives such as the Enermax T40, Raijintek Aidos, Cryorig H7 (better by far than the hyper212) all of which are smaller in height for around the same price.