No, I have a hard imagining ANY FF game being multi-player. (I've not played FF:CC on the Gamecube yet, so I'm not including that one.) For one thing, it'd only be in battles, and while I could see it being possible (though boring) with ATB system, I don't think I'll work too well with FF1. All the characters and strategies can easily be handled by one player, and all of the players would have to wait until a round of combat with the light warriors and the monsters attacking each other until they can go at it again.

It just wouldn't be fun.