I've read some studies (can't remember where or when) that at test plants (can't remember which) in greenhouses displayed increased growth rates when CO2 was increased. All I do know was that the studies were in a peer-reviewed scientific journal.
Regarding the CO2 settling issue, I believe that the temperature fluctuations in your house/tank/container would keep the gasses mixed. I think that the examples that we have heard of were of large concentrations of gasses at temperatures very different from the surrounding air, causing them to sink, until they warmed up.
The only think I might worry about is that if the system is closed, you might want to keep an eye on any non-photosynthesizing critters in there. If you have none, then don't worry. If you do, how much do you value them? If they are vertibrates, or complex invertibrates, I'd watch for signs of stress. But I think this is a cool home experiment!