I'm sorry but I don't think it would work, it would be harder to get a proper understanding of the story. One thing I like about FF being single player is that I can play through at my own pace, if a multiplayer FF were to be produced, I would have to wait till my friend is ready to play so we could both play at the same time.
Alot of multiplayer/co-op games have an option for people to drop in and out these days, so you can carry on in single player if your playing partner isn't around, then when you two are together and ready to play, they can join back in.
If a full FF multiplayer game could be possible and work, that could do aswell.
But doubt it would anyways.