If you look on the charge based models like EKV or ACM, you can seen they have nothing to do with gds for saturated transistor.
So, it does not matter in which inversion level mosfet is working, the ideal transistor has gds→0, Vds » Vdssat. It is because the normalized channel charge (and then current) is defined as a subtraction of so called forward (calculated in respect to source potential) and reverse one (calculated in respect to drain potential). In Saturation reverse part is going to 0, resulting with flat output characteristic.
As I know, the finite output resistance of mosfet is modeled by adding such things like: channel length modulation, drain induced barrier lowering and hot carrier injection.
And all of these effects are putted more or less independent to inversion region.
However, You can find that each of mentioned effects is dependent to overdrive voltage and/or affecting threshold voltage, so results with a Vgs influence on the gds.