That's exactly what the India historian, William Dalrymple, suggests in this fascinating essay for The Guardian.
According to the legend, St. Thomas came to Kerala in India in 52 CE. Stories say that he came "from Palestine by boat; that he had travelled down the Red Sea and across the Persian Gulf, and that he landed at the great Keralan port of Cranganore." And there, according to stories handed down from generation to generation, St. Thomas "converted the local Brahmins with the aid of miracles and ... built seven churches."
Are these stories true?
Dalrymple thinks that St. Thomas had the means to get there. The discovery of Roman coins in Kerala suggest the existence of a Roman trading station and the spice trade peaked at exactly the time people believe that St. Thomas arrived in Kerala.
In addition, sailors had just learned how to manage the monsoon winds that could reduce sailing time between the Middle East and India. Dalrymple notes that St. Thomas Christians in Kerala continue certain Judeo-Christian practices like circumcision and obeying Jewish food laws.
He argues that is because "it is likely that he would have taken a distinctly more Jewish form than the Gentile-friendly version developed for the Greeks of Antioch by St Paul and later exported to Europe." Oral tradition also suggests the influence of St Thomas. Songs and dances "passed on from father to son and teacher to pupil, they preserved intact many of their most ancient traditions." For these, and other reasons, Dalrymple thinks that St. Thomas may have indeed established a church in Kerala, but says that we can never know for sure.
BBC broadcast a film called "Doubting Thomas" with William Dalrymple. It is the third of a series called Indian Journeys. You can see it below