I've seen plenty of reports on electronic whine from the components on some cards. I've never had it myself.
I've always preferred the interface on Precision to what Afterburner offers. I fold on my GPUs (heavily overclocked), so all fans are set at a constant 100%, and I get nothing but the soothing whoosh of air.
This whine can usually only be heard on an otherwise quiet system. It is not loud, but the whine is absolutely annoying. Good thing is that it usually occurs just before a catastrophic failure of the part that is making the noise, so it goes away.
What makes some coolers loud is they put these stupid small fans that have to spin at 4000 to 5000 RPM just so they can have a flat plate to put a screen print picture. So, your ears suffer so there can be a pretty graphic on the video card.
Here is an example of 3 versions of a heatsink on the same card. In order of loudness.
Audible, annoying or not is up to you. This fan seems large enough to only have to spin fast, not insane
http://www.newegg.com/Product/Product.aspx?Item=N82E16814130810&name=Desktop-Graphics-Cards
Would hear air moving more so than fans but this would not intrude on any game, even in quiet areas.
http://www.newegg.com/Product/Product.aspx?Item=N82E16814130837&name=Desktop-Graphics-Cards
If they picked the right fans, you might never hear this one, even with the case sides off
http://www.newegg.com/Product/Product.aspx?Item=N82E16814127696&name=Desktop-Graphics-Cards
maybe your fans need oiled.
Or buy headphones and let them fans go 100% speed.
Can't really oil a fan, grumbling is a sure sign of bad bearings or a high pitched whine. The OP could look at the stock fan or research just what it is and it's specs. Then try to find a fan that is quieter that moves as much air.
But, your right, headphones is the way to solve this one.