Something not mentioned here is the oceans acting as a CO2 sink, taking CO2 from the air. If these volcanoes are releasing to the oceans some great amount of CO2 then that must, I would think, much alter their equations. I think that's suggested in this release and probably appears in the study.
I would think that there would be some type of equilibrium over long periods of time. IIRC, the long term reduction of atmospheric CO2 over geologic time is due to the weathering of rocks.