Influence of a magnetic field on coil impedance
The answer to your question depends on the coil.  Assuming the coil is operated at a frequency that is fixed and reasonable for its construction, and ignoring winding resistance, coils without magnetic cores ("air core inductors") have a constant impedance because the permeability of the core is unchanged regardless of the current and the resulting field strength.

Most inductors have ferromagnetic cores whose permeability varies with field strength, so your inductance will decrease as the current increases.  If you look at the magnetization curve (B-H curve) for a core material you can see that the curve flattens out as core saturates.  Coils are designed to operate in the area around the origin so that the saturation effect is not as pronounced, but there is some small effect even in this area.

In addition, losses for cores occur ("hysteresis losses") when the direction of magnetization is reversed.  So, a well-designed ferromagnetic inductor has a small variance in inductance with current that is unavoidable, as you have suggested.  The impedance will be lower (the inductance will drop) slightly as the current increases.  If the core is saturated, the inductance will drop dramatically.