No. The S-4A is a DMX device that is designed to work with a totally different set of strobe units.
If you have the Flash Shot DMX, you don't need the S-4A controller, because you already have the control IN the fixture, and teh S-4A doesn't send out additional DMX.
The S-4A is designed specifically for controlling up to 24 Super Strobe, S-100A and Snap Shot (right off the S-4A product page).
The S-4A can do some neat things that you could do via DMX though, but with this unit, it's easier, but again, it's not for DMX strobes.