I have not tried an S2 on a 5770. However today I mounted an S1 on a 5770 and then an additional S1 on a 5850.
The 5850 was easy, and the trimming to the cooler was minor. If you are willing to remove the DVI shield, you don't even have to trim the cooler.
The 5770 was a complete PITA and involved major cutting. The problem is that the GPU is much closer to the back panel on the 5770 than on the 5850. Comparing the S1 & S2, it looks like you would need to trim most of the fins between the heat-pipe and the display connectors, although this will still leave *plenty* of surface area to keep a 5770 cool. With the S1, I wound-up removing about half of the fins from the outer heat-pipe and then bending the "naked" copper pipe to clear the DVI connector. This took a lot longer than I expected, and I had to remove the DVI connector shield permanently.
In both cases the final outcome is excellent. The stock cooler on both the 5770 and 5850 is *not* silent at idle, but with the "turbo module" fans mounted (which I can't hear), the S1 keeps both cards under 67C during a Furmark run. Considering that the stock coolers scream like Banshee's under heavy load and temps still push 80C+, an after-market cooler is an excellent upgrade.