The comma doesn't make any difference

Quite the otherwise. Without the comma it is a restrictive clause and *would be saying that the Welsh were descended from the very people to whom Paul had written one of his little diatribes. With it it merely identifies the Galatians, from whom the Welsh were putatively descended, as those people, a subset of to whom Paul wrote.

Whether the Welsh were, in fact, descended from the same people who populated the burg of Galatia is a whole nother question.