I think you could hear it unless there was another noise of a nearby frequency at the same time (which is entirely possible with voices and possibly fork-and-knife-on-plate noises). But for the sake of argument, let's assume that it was a ballroom full of men with deep voices and no other high-frequency sound producers.
Think of the triangle in an orchestra - it's not a loud instrument, but it's one that can definitely be heard above the sound of the rest of the instruments. That's because none of the other instruments are making sound in same range as the triangle. Assuming that there's no sound interference from another source, it's entirely possible that you could hear your friend's digital watch go off. There are a lot of assumptions in that statement, I'll admit, but here's a bald fact - your friend should invest in a real watch if he's going to places like ballrooms.
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