Seeing as how they're different size batteries, the answer is a flat-out no. They Skyrocket has an 1850mah battery, and the SGIII is 2100.
The mA makes no difference. I have a 3300mA battery in my S2 with an extended case, plus I have the 2250mA battery from the GNex that fits with the normal case backing. And then there is the original battery with NFC chip. All work just fine, as they are all 3.7v.
It is physical dimensions and pos/neg pin placement that matters. When I get my S3 in 2 weeks, I will know for certain.