Can I replace an old closet light with multiple electrical outlets?
The best answer to this is to leave the light as a light and have a qualified electrician run a three wire circuit (hot, neutral, ground) direct to your soon-to-be office. Your modern equipment needs it and disturbing any old turn of the century wiring is asking for disaster. 

Having lived in an old house with Range, Pump and four circuits, adding any extra load to an ancient system without upgrading the wiring is a good indicator for having several fire detectors located in strategic places and keeping their batteries up to date.