What would happen if we could revert $\mathrm{CO}_2$ production but took it too far? So recently, scientists managed to produce fuel basically out of thin air (water, air and sunlight).

And in a discussion I had with a friend, the question came up, what would happen if you took that idea too far?

Say you could build an air-to-fuel plant large and efficient enough to take CO2 out of the atmosphere faster than all the things we currently do to increase CO2 levels add it in.

What would happen? First of all, how far could you realistically even take this: Would it be possible with the used process to go all the way down to 0 atmospheric CO2 (or at least approach this arbitrarily closely)? And what effects would this have on the environment?

I immediately had three ideas that could happen but I wonder how realistic those would be:


Average temperatures would drop (inverse Greenhouse effect) (but how far?)
Plants would eventually be unable to produce sugar through photosynthesis and die off
Instead of acidifying, oceans would become increasingly alkaline. Lime might drop out of the oceans rapidly which could, perhaps, have cancer-like effects on coral reefs and anything that heavily depends on lime.


And besides those, are there any other obvious notable effects?
The average global warming due to greenhouse gases corresponds to a 33 Kelvin temperature increase.  If you remove all greenhouse gases the average global temperature would then decrease 33 Kelvin (from 288K to 255K).  

You might want to check out:
http://www.nasa.gov/topics/earth/features/co2-temperature.html
 which estimates the CO2 portion of global warming to be about 80%.


  "... it is the 25 percent non-condensing greenhouse gas component, which includes carbon dioxide, that is the key factor in sustaining Earth’s greenhouse effect. By this accounting, carbon dioxide is responsible for 80 percent of the radiative forcing that sustains the Earth’s greenhouse effect."


Simple math might suggest then that the average global temperature of Earth would be ~262K if CO2 were completely removed.  There are always sources of CO2 though, so you could never remove it all as it is constantly being replenished when animals breathe and things burn.