Although I haven't used CO2 personally, it doesn't seem like a problem from what I understand.
Is the divider a solid unventilated piece, or more like a mesh? Assuming there is some way for the water to flow between the two sides (and if it wasn't I imagine that would cause problems with filtration, unless you have something for that on both sides), I can't think of any reason to diffuse on both sides, since the idea is for CO2 to dissolve in the water. The CO2 should diffuse freely throughout the tank after it dissolves, like a drop of food coloring would, especially since the tank is fairly small.
--Keeping fish is easy--
--Keeping fish alive is a different matter--