All math points towards surface agitation and the exchange of O2 and CO2. So yes, having an airstone is rather mute and in my opinion will gas off most of your CO2. I wouldn't honestly run one at night either. If you're heavily planted, which I assume you are, hence why you're injecting CO2, your plants are putting off enough oxygen to keep the fish breathing at night, plus with your surface agitation from your filter is enough to make the exchange.
I would never run an airstone in a tank I injected with CO2.
Plants give off oxygen during photosynthesis. So, when there is no light to drive photosynthesis, no oxygen.
Photosynthesis creates starches that are stored for later use. This starch is broken down into sugars and converted to energy. This process uses oxygen and releases CO2 and is not light-dependant. So it continues during the night.
Typically, plants produce more O2 than CO2 in a given 24 hr. period. However, O2 gets used by fish, bacteria, and plants. At night, O2 levels can drop very low in a heavily planted tank.
During periods of darkness, aeration is recommended and CO2 injection is not very useful.
During daylight hours, aeration should be reduced or eliminated if there is sufficient surface agitation, surface area, and plants producing O2 to support bacteria and animal life.