I don't know enough to comment on the question, but can comment on the comments.
For the first time, I find myself in agreement with Jim, but Nola is just talking out of his own private volcanic eruption.
"Saturation" is too simple a concept, since we have equilibria (or systems more or less trending towards equilibria) involving solid limestone,dissolved carbonate, dissolved hydrogencarbonate (a.k.a. bicarbonate), "carbonic acid" which is simply carbon dioxide dissolved in water (I know that elementary chem textbooks say different), and CO2 in the atmosphere.
At any given temperature, the equilibrium amount of CO2 dissolved in water is proportional to pressure, as required by Henry's Law, but this solubility decreases with increasing temperature, which I think is the main reason why warming for any cause is expected to be followed by release of CO2 into the atmosphere, generating the positive feedback loop.
Most of these equilibria are established quite rapidly locally, although equilibria involving calcium carbonate can be much slower, and organisms generally rely on the oceans being supersaturated in calcium carbonate in order to build their shells.
However, because the oceans are large, diffusion, heat energy transfer, and turnover are slow (time period around 1000 years), giving long time lags.
As Einstein may or may not have said, every scientific problem should be made as simple as possible, and no simpler.