According to Corsair, the Corsair 600T can fit a cpu cooler of a maximum of 160mm height. According to Newegg, the Noctua NH-D14 is exactly 160mm in height. So yes, it should fit, although just barely.
I would at least look at water coolers if you're looking at expensive air coolers. They are supposedly both 160mm, so it should fit, though I wouldn't guarantee it.