I've heard Baba inspires people to visit him. Is there a story that illustrates this and what happens when they arrive with doubt?

Yes, Chapter 35 illustrates this perfectly. The text explicitly states that Baba himself gives people the inspiration to visit, leading them toward the spiritual path. The story then focuses on Boss Dharamsee, who was driven by curiosity but arrived full of skepticism. His initial experience was one of internal conflict, as he disliked the seeded grapes Baba offered and mentally challenged the saint's omniscience. However, as Chapter 35 beautifully narrates, Baba knew his thoughts and engineered a miracle where the grapes became seedless. This experience caused Dharamsee's ego to vanish, and "love for Sai arose in his heart," turning his visit into a firm resolve to return.