The headphones will actively remove (a little bit of) white noise from your environment (air conditioners, server fans, etc) which in practice actually makes 'signal' type noises more audible. I've noticed, for example, that I can hear the flight attendants on the intercom much better with my noise cancelling headphones on than without because the noise from the engine is partially cancelled.
I can see how heavy over-the-ear headphones would help in that they will dampen all noise, especially if you add in some white noise on top of that.