Its possible that the tradition of Saint Thomas had a historical basis. However, its very unlikely that the Christian community in Kerala dates to such an early period.
The story you're referring to is from the Acts of St Thomas. This is a new testament apocrypha, or a non-canonical work, dated to the 3rd century. The most compelling part of the story is that it correctly names the ruler in North India, Gondopharnes. This is significant because we didn't know anything about him or most Kushan rulers until they were discovered by modern archaeology and numismatics. This means that it probably does represent a tradition near contemporary to the time in which it is set.
The details of the story are quite probable. He accompanied a businessman. He first stayed at the court of Gondopharnes, then traveled to South India where he spent the rest of his life. The amiability of Gondopharnes to Christianity may be represented by the fact that he became one of the three kings in the new testament.