common mode choke on DC line
A common mode choke on a DC line will normally be passing some DC current through one winding and the same (but in reverse) DC current back through the other winding thus it is allowing power through the choke with very little hindrance. Under these circumstances, the magnetic flux in the core is cancelled and therefore there can be very little saturation of the core that might lead to a reduction in inductance.

It's the same scenario for AC - at any point in the alternating cycle, the current passing into one winding is the same as the current being returned by the load and therefore it is passing back through the (reversed) second winding. This offers a very small impedance to normal power currents passing to the load.

In both these cases flux largely cancels but, in the case of a common mode current, flux doesn't cancel hence the choke "offers" a significant impedance and this attenuates the common-mode current up to the point at which saturation starts to occur.

Short story: AC and DC current being passed to a load do not affect common-mode inductance.