The only Sega CD game I've got that makes use of a mouse is D&D: Eye of the Beholder. It makes sense there, because that game uses a cursor. SF games don't really benefit from that kind of precise movement. Beholder also has a "Mega Mouse" logo on the back of the box, while SFCD does not, nor does its manual mention the mouse at all.
The mouse itself was a three-button deal (that's three full buttons, now two and a clickable wheel), plus a start button below the left one. I assume that a game has to be designed to recognize directional input from the trackball, and SFCD isn't one of those games.
Knowing is only half the battle.
So you still lose.