The FGW Converter polls the controller every 5ms, over 3 times per frame, and no affect on gameplay. The only way around that would be to crack open the Saturn pad, disable or remove the existing electronics and run the signal wires out of the pad to solder onto a common ground Xbox360 pad, making it pretty much a monstrosity. But it’s an option.
The way I’d recommend would be to get an FGW Converter, a Saturn extension cable (so you can cut and use the female end) , a common ground Xbox360 pad (MadCatz Fightpad preferred), and a box to put it in. The final product would be a box with a USB cord coming out one end to go into the Xbox360, and the female Saturn cord coming out the other end, making it a dedicated Saturn->Xbox360 converter. No Saturn pads, hallowed be thy name, would be destroyed in the process. (I get crabby when I see people destroying old pads that arent made anymore, especially classics like Saturn, SNES, and NES pads.)