Good thing plants eat carbon dioxide then, so we don't need to wait for it to break down by itself. The more CO2 in the atmosphere, the more plants grow and convert it to oxygen.
Plants only store the CO2 until they decompose a relatively short time later. The only way to end up with a net decrease in CO2 this way is to bury the plants deep. Of course that is the process that initially created coal.
The amplitude of the world's natural CO2 cycle is on par with about 1.5 years of anthropogenic emission. Which is certainly impressive, but it's cylic and fairly steady. Plants are not growing fast enough to support the fantasy you describe.
It's 300-1000 years [1].
[1] https://climate.nasa.gov/news/2915/the-atmosphere-getting-a-...