No need to run a skimmer on something without a bioload, however it won't hurt either if you wanted to.
But please, don't cycle a new tank with fish like some recommend. This isn't 1985, we have dozens of better and less cruel methods of cycling a tank, like adding beneficial bacteria (though some say it's just snake oil).
Either way, the best/easiest way to cycle a tank is to add ammonia and then test a few times a week until all ammonia and nitrites read zero and there's a nitrate reading, then do a waterchange to drop nitrates to a safe level and you're good to go.
So to answer your question specifically, no you don't have to run a protein skimmer yet, but yes, you can.