I assume then that you have a pre-07 vehicle, as 07 and up (Maybe earlier, don't know) uses electric fans. And from what you say it looks like you know you have one...
Anyway, I'm not sure on yours, but the one's I've seen are thermostatic, meaning they are activate by heat. On these you can usually see the spring on the front of it. The other kind is non-thermal, and they spin more at low rpm and very little at high rpm; so yeah they are speed operated. Both have fluid in them. Only the second one is going to spin on cold start up, I think. I've seen them fail, and usually it's indicated by either a fluid leak or looseness/play from bearing failure. I suppose there could be noise associated with bearing failure, but is it loose when you shake it side to side? From what you're saying I don't think fan clutch drag would affect the other accessories on the pulley line, because its function is forward of the pulley, and I'd be more suspicious of the water pump, since it is. BTW, if it is bad, it can fail the water pump, and vice-versa, since they share an axle. I'd want to narrow it down correctly, one way is to wiggle it back and forth for play, another is to stethoscope (or screwdriver with handle to your ear) touching different areas with it (being VERY CAREFUL not to touch the belt/pulley/fan!), to find where that noise is coming from. Then again, fan clutches and water pumps aren't very expensive, so if they have some miles on them I'd be ready to replace them in a heart-beat... this is your cooling we're talking about here. But I don't know that what you describe indicates the clutch or not; it could be the belt, another bad tensioner, the A/C compressor, clutch, belt alignment, or anything until you narrow it down properly.