I have used an Accelero S1 with a *single* 5850: not so power hungry, but not that far from a 5870 once a bit overclocked.
Definitely, with the S1 VRM cooling will be your main problem. I used a pair of 120x25 mm of Gentle Typhoons at around 600/700 rpms, as well as 80x25 Noiseblocker multiframe at around 800 and it worked... but, you won't be able to overclock much, and you will probably not be able to pass furmark, unless you use a PWM fan that can be powered/controlled via the graphics card connector and can spin faster in the rare events where you have not enough air flow (yes, furmark and probably nothing else).
You'll have to make sure the fans are blowing directly on top of the VRM area. And, I'm not sure about one fan being enough: but a pair of 92/120 mm fans spinning at 500 to 700 rpms will work nicely (again, furmark will probably be too much).
Now, about the Crossfire thing, that is much more complicated. I'm not sure it will work, especially because the cards will be so near that the one on top will probably starve for airflow and receive lots of hot air. *If* it works, I'm 99% sure you'll need to use PWM fans, as you will not be able to keep up with the fans at a fixed low speed when you are gaming. And, of course, you will need to provide custom fan speed curves, the ones provided by default will probably not be adequate.
Now, just FYI, and as an alternative...
I am using a pair of 5850 with Accelero Xtreme Plus in Crossfire, with three slots in between (not the typical two, that is too tight, and even more for an S1), and I can tell you it works well: it is dead quiet (I would say silent) at full load and very effective.
Admittedly, I have a case I modded for extreme quietness and good airflow, with 4 500/600 rpm 14 cm fans blowing over the crossfire cards and a 12 cm @ 600 rpm exhaust fan I managed to place in the PCI slots area. So, do not expect silent crossfire in a typical config...but you might be able to get a very quiet config