When my 5850 (and 5870) fans fail, I just pop off the cowling, strap an 80mm casefan to the HSF unit with zip ties and fire it up. Keeps the cards cooler than stock fan, looks ghetto as hell, but works great and its' cheap/easy to replace if/when the fan fails again.
Not sure thats a good idea with all cards. Some have a "closed heatsink". If you look at the card as you normally would when its laying flat on a table, underneath the shroud you basically see a solid metal sheet with just a hole for the fan. The fan forces the air through the vents that you cant see from the top. Blowing on to that sheet is probably rather pointless. non reference XFX cards are like that. I had to put 3 case fans in series to keep a dead fan 5870 from melting. If Im not mistaken 5850 and 5870 reference coolers, while different are also mostly closed on the top.
Other cards have an "open heatsink" where the plastic shroud is actually needed to force the air through the vents of the HSF. In that case Im sure strapping on some case fans would work great and probably better than stock in an open rig.