Indeed a tricky question.
Permanent magnets have been used to bias inductors closer to saturation in ferroresonant power supplies, particularly in the TV industry. Also they find use in TV inductors to create a degree of non linearity.
There are many qualifiers here e.g. what is the intended frequency of operation? this will determine the type of magnet that may be used without suffering significant eddy current losses at high frequencies, ruling out sintered metal alloys such as Alnico or Samarium Cobalt over ceramic based magnets, which have an insulating binder by nature of manufacturing and design.
There also is the demagnetizing that will occur if certain types are operated at very high power levels.
Temperature stability is also an issue since magnets flux varies with temperature in certain types, and this factor is used to temperature compensate ferroresonant power supplies.
The simple answer is yes it will perform as an inductor core, but in the design, consideration must be given to the intended use of the inductor.
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