I wear a modern ANR headset, with very good passive noise reduction too, and the trim wheel is absolutely clearly audible over all the other flight deck noises. Unlikely that it could be missed (but obviously not impossible) but more likely it simply doesn't attract attention with it being a familiar noise at this phase of flight. A crew would have to recognise the trim running for an unusual length of time, but with other more "urgent" distractions such as weather, or a degredation in capacity due to fatigue, I could accept it as a possibility.
Perhaps we should also keep in mind that when humans become maxed out with a task the first sensual input the brain deletes is that of hearing.