I've heard that one should not go empty-handed when visiting a Guru. Is this mentioned in the stories of Sai Baba?

Yes, this tradition is mentioned in Chapter 35. The text explicitly states, 'It is not good to go empty-handed to the door of God, a priest, or a Guru.' Following this principle, a devotee named Kaka bought two seers of grapes to offer to Sai Baba upon his arrival in Shirdi. He then placed his head at Baba's feet and offered the grapes into his hands. This act of bringing an offering is presented as a proper and respectful gesture when approaching a spiritual master, setting the stage for the subsequent events in the story.