I have a Silverstone ML08 (with handle) sitting on my desk... so it's pretty much worst case scenario for hearing sound from the GPU. Unfortunately, with the space I have to work with and pets and small kids it has to go on the desk. I also take it to my friend's place every week to play games, so it needs to be easily accessible. In fact, my last build was a giant Fractal XL-R2, and I specifically built this machine with the intention of having a silent, portable system that would fit nicely up on my desk. I had no idea that I was getting a graphics card that would make noises during the idle fan off mode. From my research, it seems that this problem is specific to EVGA - other card makers' fans are actually idle at idle. The fact that my 1070's fans remain motionless after a reboot suggests that it's at least possible in theory for it to stay still too. But as soon as the fans are spun up (either due to a gaming load or if I turn the fans on in PrecisionX), when the card returns to idle, the fans twitch.
I tried setting a fan curve to spin the fans constantly at the lowest speed (<10% duty), but the ball bearing fans used in the ACX 3.0 are relatively loud even at the lowest possible speed. The only fan I have going in the system is the CPU fan on my Scythe Big Shuriken II, and it's perfectly silent at 500-600 RPM, while the ACX hisses and chatters audibly at 300 RPM.