Current carbon dioxide content of Earth's atmosphere is, after more than a century of burning fossil fuels, 0.0000407 atmosphere.
Pretty much negligible for the purposes of the game.
Not really. Since the game considers it harmful at 0.005 atmospheres (or 5000ppm), and that 407 ppm represents 0.000407 atmospheres, not 0.0000407.
It is true that right now we are in reality adding about 3 ppm / year meaning we would reach Aurora harmful levels after 1531 years, but I'm not sure how realistic the Aurora 4x model of CO2 as a greenhouse gas is, and the temperature increase is another thing to consider (melting of ice caps). If current addition rate was negligible I doubt it would be such a debate as seen currently.
Even given the current model it's not unimaginable to have an Aurora 4X fossil fuel based conventional industry 10-20 times larger then that which we have on Earth now, which would reach it in 150 or 75 years.
Something else to consider is that the rate of CO2 addition is speeding up, a 100 years ago we were adding about 10% per year compared to now, and it shows no sign of stopping, so if the exponential increase continues we are looking at a rate of 30 ppm / year not to far away into the future.
It seems like it wouldn't be such a hard thing to add, and would add a few interesting stories or scenarios you can play out.