It depends on the stairwell.
How many stories?
Do you know if it's a rated stairwell?
Any idea what this receptacle is for?
Where I'm going is if it's a rated stairwell as part of a required means of egress, nothing is allowed in that stairwell except that necessary for egress. This includes risers & treads, landings, lighting, handrails & guardrails, exit signs, sprinklers if sprinkled, smoke control system if high rise, etc.
If you want a receptacle in there for the cleaning lady to plug in her vacuum, check with your AHJ and see how they interpret that. One argument is that it's necessary to keep the stairwell maintained and another argument is that it's an undue risk and she can run a cord if she doesn't smash it in the door. It's a matter of how AHJ interprets it.
And AHJ on that issue is bldg. inspector (bldg. code) and fire marshal (life safety code). I don't know if the NEC addresses this or not, but if so, your electrical inspector too.