Anthropogenic carbon dioxide (CO2) emissions are acidifying the ocean, affecting calcification rates in pelagic organisms, and thereby modifying the oceanic carbon and alkalinity cycles. However, the responses of pelagic calcifying organisms to acidification vary widely between species, contributing uncertainty to predictions of atmospheric CO2 and the resulting climate change. At the same time, ocean warming caused by rising CO2 is expected to drive increased growth rates of all pelagic organisms, including calcifiers. It thus remains unclear whether anthropogenic CO2 emissions will ultimately increase or decrease pelagic calcification rates. Here, we assess the importance of this uncertainty by introducing a dependence of calcium carbonate (CaCO3) production on calcite saturation state (ΩCaCO3) in an intermediate complexity coupled carbon-climate model. In a series of model simulations, we examine the impact of several variants of this dependence on global ocean carbon cycling between 1800 and 3500 under two different CO2 emissions scenarios. Introducing a calcification-saturation state dependence has a significant effect on the vertical and surface horizontal alkalinity gradients, as well as on the removal of alkalinity from the ocean through CaCO3 burial. These changes result in an additional oceanic uptake of carbon when calcification depends on ΩCaCO3 (of up to 270 Pg C), compared to the case where calcification does not depend on acidification. In turn, this response causes a reduction of global surface air temperature of up to 0.4 °C in year 3500. Different versions of the model produced varying results, and narrowing this range of uncertainty will require better understanding of both temperature and acidification effects on pelagic calcifiers. Nevertheless, our results suggest that alkalinity observations can be used to constrain model results, and may not be consistent with the model versions that simulated stronger responses of CaCO3 production to changing saturation state.