Carbon cycle models used to calculate the marine reservoir age of the non-polar surface ocean (called Marine20) out of IntCal20, the compilation of atmospheric C, have so far neglected a key aspect of the millennial-scale variability connected with the thermal bipolar seesaw: changes in the strength of the Atlantic meridional overturning circulation (AMOC) related to Dansgaard/Oeschger and Heinrich events. Here we implement such AMOC changes in the carbon cycle box model BICYCLE-SE to investigate how model performance over the last 55 kyr is affected, in particular with respect to available 14C and CO2 data. Constraints from deep ocean 14C data suggest that the AMOC in the model during Heinrich stadial 1 needs to be highly reduced or even completely shutdown. Ocean circulation and sea ice coverage combined are the processes that almost completely explain the simulated changes in deep ocean 14C age, and these are also responsible for a glacial drawdown of ∼60 ppm of atmospheric CO2. We find that the implementation of abrupt reductions in AMOC during Greenland stadials in the model setup that was previously used for the calculation of Marine20 leads to differences of less than ±100 14C yrs. The representation of AMOC changes therefore appears to be of minor importance for deriving non-polar mean ocean radiocarbon calibration products such as Marine20, where atmospheric carbon cycle variables are forced by reconstructions. However, simulated atmospheric CO2 exhibits minima during AMOC reductions in Heinrich stadials, in disagreement with ice core data. This mismatch supports previous suggestions that millennial-scale changes in CO2 were probably not driven directly by the AMOC, but rather by biological and physical processes in the Southern Ocean and by contributions from variable land carbon storage.