Alongside the ACC there is also the associated Meridional Overturning Circulation (MOC), which is also mainly driven by wind forcing. The insensitivity of the mean current to the accelerating wind forcing can also be seen in the MOC. This near independence of the MOC to the increase of wind stress is referred to as eddy compensation. There would be perfect eddy compensation when the Ekman transport would be balanced by eddy-induced transport.
There is a widespread belief that the sensitivities of the transport in the ACC and MOC are dynamically linked. However, note that eddy saturation and eddy compensation are distinct dynamical mechanisms. Occurrence of one does not necessarily entail the occurrence of the other. It is hypothesized that dearth of a dynamical link between eddy saturation and eddy compensation is a consequence of the depth dependence (cancellation between the  Eulerian circulation and eddy-induced circulation). Currently it is assumed that the ACC is fully eddy saturated, but only partially eddy compensated. The degree to which there is eddy compensation in the Southern Ocean is currently unknown.