Do you need a grommet to protect electrical wiring run through a hole cut in a metal stud?

Ideally yes. Any potential for the cabling to move against the edges of the hole will cause shorting out and potential fire hazard as well as electrocution.

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The electrical code does not allow home cable (loomex) to be used in non combustible buildings. If metal studs are used throughout a commercial building then BX has to be used. There are grommets that make pulling the BX through the metal studs much more easier. To save labour on the job the grommets are highly recommended. They can be installed as the holes in the studs are punched out.