Hey RowdyNoe, I'm not a mechanic by trade, but I've done a lot of auto work, inc. on my 2004 F250 PSD.
So, not wanting to degrade anybody's advice, but in my experiences, a fan with a clutch will still turn when engine is running.
As I have been told, the fan clutch on these trucks is an electric clutch that, at temp, "locks up" to provide added air when needed.
Now, with that being said, if your clutch is bad, then when the engine needs added cooling, like towing up a hill, hot air temps, etc, then your clutch may not "lock up" as it should.
You didn't say, but is this "helicopter" sound all the time, or just on occasion? Is the sound steady or a "woosh-woosh" sound?