I was thinking along the same lines as jake. But I arrived at my answer thinking that the carbon dioxide will transfer heat less effectively than the liquid, so the heat transfer will be slightly affected. Thus the ice cubes should melt slower.
But of course as jake said, this is only one possibility; several actions could counter this and make the opposite occur.
my suggestion would be to buy some carbonated water and some plain water, and chill then both in the fridge for a few hours so that they're at roughly equal temperatues. get some ice cubes of the same approximate size, and time how long each one takes to melt. repeat a few times.