Theoretical arguments and idealized ocean-only simulations predict a relationship between increased sea ice formation, enhanced buoyancy loss rates, stronger deep ocean stratification and shoaling of the glacial upper overturning cell, as suggested by proxy data of the Last Glacial Maximum. Here, we test whether this mechanism also holds in an ensemble of higher complexity coupled climate simulations. These fully-coupled ensembles are generally characterized by substantial discrepancies in the simulation of glacial ocean circulation between different models, often at odds with the geological evidence. We show that these apparent inconsistencies can in large part be attributed to differing (and likely insufficient) formation and export of Antarctic sea ice. Such biases are further amplified by short integration times, as the transient response of the deep ocean circulation to surface cooling differs fundamentally from the near-equilibrium response, which is instead expected to be more representative of glacial climates.