No, you the visuals of the game wouldn't look better with a 120hz refresh rate, but if you could pull a steady 120fps it would certainly feel smoother. Can't pull off 100+ FPS even in deserted areas with a 290x (I heard this game performs poorer on AMD cards though) but I cap it at 60 (60hz monitor).
If this really isn't a bragging thread, and you want the game to look nicer with decent FPS I'd recommend going for an ultrawide monitor + a GTX 980. No idea how FFXIV looks on an ultrawide monitor, but a friend has one and some games look spectacular on it.
