The purpose in adding CO2 is to get more carbon dioxide into the water, presumably to increase plant growth or sometimes to lower the pH (it does this notwithstanding). Any device that causes surface disturbance or excessive water movement increases the exchange of gasses at the surface, by expelling CO2 faster and bringing oxygen in faster. So in this regard, the two systems are working at cross purposes.
Assuming your use of CO2 is for plant growth, this can only help during the daylight since plants do not photosynthesize during darkness. Therefore, CO2 diffusion is usually turned off during darkness, otherwise it is just wasted and may cause a serious depletion of oxygen. At the same time, those with heavily planted tanks sometimes suggest running an airstone at night to ensure sufficient oxygen. This is only necessary in tanks with CO2 diffusion during the day.