Swami Vivekananda before his chicago visit made a visit to south india, while southern Indian trip itself is very interesting as he even wrote about it a lot, I want to focus on his Kanyakumari visit specifically. In Kanyakumari, he visited Mother Parvati's temple and then went to meditate on the rock which was purified why Mother Goddess' feet Herself. I have read that he had visions of India's past and 1000 years(not sure) future of Bharata. In the end he was tearful , tears of happiness and pride about India. Even today Vivekananda Rock Memorial is maintained there by Vivekananda Kendra built by strong efforts of Eknath Ranade.
It was due to this incident only, that Swami Vivekananda was full of confidence for his foreign visit.
Now coming to my question, In one quora post, I read how when Vivekananda was questioned by some Hindu monks about future of Hinduism since they feared the conversion activities of missionaries. It was writte there that Vivekananda smiled and assured them that in the future Hinduism will be popular throughout the world with Vedanta forming the basis of it. Even people will convert to Hinduism with no caste and will known as Vaishnavas. It was written there that this vision he had during his time in Kanyakumari.
So my question is, Is this incident about Swami Vivekananda prophecies of Hinduism true? Also what exact vision he had about future of India and Hinduism that made him cry in joy?