It`s unlikely, but it`s a mechanical part, and so can be susceptible to failure.

Undo the screw on the top of it to bleed any air from the feed line, and hook a drill to the shaft and spin it up to see if oil flows from the injector nozzles.

You won`t get a stream from them, you`ll just sort of get `drips`. Haven`t seen many genuinely failed oil pumps.
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