Quoting myself from a previous answer to a similar question:

In Origin of India's St. Thomas Christians: A Historiographical Critique, Benedict Vadakkekara comes to the conclusion (as others have before) that, considering that there was frequent trade between the Middle East and India, the age and consistency of the tradition, and some recent archaeological discoveries, it would be possible, even probable, that Thomas the Apostle preached in India and founded a Christian community. However, he believes there is not sufficient historical evidence to declare it a certainty.

This echoes Samuel Hugh Moffett's position that "given the difficulty of proving a negative answer and an equal hesitation to accept unwritten traditions without some reservation, most opinions range from 'possible' to 'probable,' with a discernible trend toward the latter position since the discovery of the Gundaphar [Gondophares] evidence and renewal of interest in oral tradition as a source of history."

Very unlikely. There are varying traditions about Saint Thomas, saying he ended up in Parthia or Edessa. The legend of him going to India originates in the early-third-century Acts of Thomas, a fanciful story with almost certainly no historicity whatsoever. (It ends with evil king Misdaeus using dust from Thomas's tomb to cure his son of demon possession.)

It would be helpful if you specified which St. Thomas you are talking about; there are several.