Were there times when Lord Vitthal actually appeared in Shirdi? What do the texts say about it?

Yes, the scriptures describe several instances where Lord Vitthal's presence was manifested in Shirdi, underscoring Sai Baba's teaching that faith is paramount. Chapter 4 details how Baba promised Das Ganu that "the form of Vitthal will appear" if the devotee is full of faith. True to His word, Das Ganu was blessed with a vision of Vitthal in Shirdi at the conclusion of a week-long recitation (Saptah). In another account, Kakasaheb Dixit had a vision of Vitthal during his private meditation. When he later went to see Baba, Baba confirmed the experience by asking if "Vitthal Patil had come." This divine event was further solidified when a vendor arrived with pictures of Vitthal, and one image was an exact match of Dixit's vision, which he then purchased for worship.