Depends on the pump. Sometimes you get one that's just plain noisy. The one in my Mustang is the loudest sound in the car at idle, and has been for years ... at least since I took out what little sound deadening there was in the back. Noisy, but no problems at all. On the other hand, the one in the Bronco was quiet even when it died. :banghead
My pump diagnosis method is usually "run it til it quits, then you know it's bad." That might not work so well if you spend a lot of time in places where you really don't want it to die on ya, though.
I never hear the one in my Bronco or Honda however, the one in my son's S10 can be heard from about 50' away. He was thinking of changing his and I asked him why, at least this way he'll know when it quits working.