Um, I guess if you have enough heat to crack CO2 you'd have some ozone forming, which is toxic and a short lived greenhouse gas. Another problem is, if you are doing this with normal air, you'd probably also get nitrogen oxide forming, which is a long lasting greenhouse gas. If you want to crack CO2 the easiest way might be to just grow some plants.

I suppose you could have a combined nuclear/coal plant. The nuclear plant would provided baseload power while the coal plant produces synthetic gas from coal that is stored and used for peak power. During periods of low power use nuclear power could be used to crack CO2 produced from the coal side of things. However, I think it would be easier to just bury the CO2, or perhaps use it to produce synthetic liquid fuel if the market price is high enough. (People are currently willing to pay over ten times more for liquid fuel they can burn in their cars than for the same amount of energy in a lump of high grade coal.)