As close as that is, it's very hard to say exactly. While the cooler height isn't in question, often the case clearance Is.
Case manufacturers will often use a standard dimension, when in reality that dimension may include a 'safe' area which can easily be 5mm or more clearance. A metal panel side will often have a different clearance height than a TG, just because of how they are mounted. And that's not including any sound baffle on the metal side.
There's multiple instances of cases claiming 155mm of clearance, and ppl using a 160mm tall CM Hyper212, with about 1mm to spare.
Generally ppl go by the stats as presented, drawing a hard line at yes or no depending on the numbers, but that's also a safe bet. With just 3mm disparity, there's a chance it will fit, just as there's a chance it won't. But it is TG, so should not be forced or touching enough to possibly cause scratches in the glass or you'll find out the hard way about the downsides to TG.