Yes, but you need to have a writer there from the get-go, and you have to make storylines work within the context of one on one and two on two fights. Most writers are avoidant of this, and most fighting games as a result have ridiculous stories attempting to explain it all. If I had to pick a game that would have a good story for a fighting game, I'd say Karateka. Same goes for Infinite Blade. They aren't necessarily street fighter, but are effectively fighting games in their own right.