How important is saturation current for an inductor?
What they're telling you with the saturation current is that above 1.6A, the core can't take any more magnetic flux, and this translates into a change in the effective inductance when the current gets into that realm. You can put more current through the winding, and you do get more flux as a result, but the effective permeability of the core drops off.

The effect won't be a sharp break, either; you would start to see some of the effects as you get near the saturation point. If you apply a pure sine wave voltage across the coil that would result in less than 1.3A peaks, the current will also be sinusoidal, but if you run the voltage up to where the peak currents would reach saturation, the current waveform will have a significant harmonic component.