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Not quite the traditional castaway rescue, but there was the case of the Meermin slave mutiny, where the imprisoned slavers used a message in a bottle to alert shore forces to the slave mutiny, resulting in the defeat of the slaves and rescue of the slavers.
There's also the case of Chunosuke Matsuyama, where a shipwrecked Japanese seaman sent a message in a bottle in 1784. Unfortunately, it was not discovered until 1935; ironically in the village of his birth.
Other stories can be found in Wikipedia, although none tell of castaways actually rescued because of a message in a bottle. It seems to be more a tradition of literature...