In fact, unequivocally yes!
But not usually to a significant degree.
In the absence of any quirky weasel conditions, like corrosion or residual magnetization or fault conditions.
Ferromagnetic materials age over time. The permeability drops approximately as log(time) since the material was last cooled below the Curie temperature.
This effect is more familiar in ferroelectric materials: type 2 dielectrics (ceramic capacitors with X7R, Y5P, Z5U, etc. codes). There, aging is very pronounced because the "core" is "ungapped", i.e., the electric field is applied to the dielectric and nothing else. This is why the energy storage capability is one of the worst, among all capacitor types. They are optimized for low impedance under 0V bias conditions, and that's it. (Precisely the same as ferrite beads, which are optimized for high impedance under 0A bias conditions!)
Inductors don't normally suffer from aging, because the core is almost always gapped, which reduces losses and improves stability (making the change in permeability less significant). Under carefully controlled conditions (stable temperature and humidity), you might be able to measure this change on a real part. It will be small, less than 1%.
Tim
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