Unless the rest of your machine is fanless or very very quiet, I would be very suprised if you'd notice something like a HD 5850 at idle in your case. If it is silent or very quite, you certainly will notice!
I use that as an example because I own one, but similarly, my HD 4850 with the Asus Glaciator non reference hsf was not discernable over the noise from an Antec Earthwatts 500W PSU, stock Q6600 hsf and two low-rpm 120mm case fans in an Antec Sonata III case, and that's a reasonably quiet case and setup I think?
My 5850 idles (ie all desktop 2d work, and as far as I am aware doesn't bump up for HDTV or DVDs) at 21% fan speed, and I can't hear it at all over my case fans until about 33%. For interest's sake, it is currently holding my card at 85'C GPU temp at 37% fans speed in furmark, and that is discernable as a low whooshing noise, that you certainly don't notice while gaming with the speakers on in any event.
Since it idles very cool at that 21% of fan speed (around 37-43'C idle temps depending on ambient in the couple of months or so I have owned it), I presume you could easily create a custom fan profile using something like MSI Afterburner (works with all ATi/AMD cards I think) to have the fan idle slower than that quite safely...
My old 4850 with the non reference Asus Glaciator fan was not discernable over my case fans even at 100% fan speed, so I left it at that at that all the time, and I think high-end cards like Sapphire's Toxic 5870 and 5850 are very quiet at idle (and load), so maybe a non-reference card is what you could look for, and then create a custom fan profile to drop the fan speed even lower?
My 2c for what it's worth
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