Hmm, medieval period was over by 1492. No mention of Vikings returning with them that I have found.
Wikipedia says the rumor is that Spain brought them to the middle-east, where they came back to England with a "meat from Turkey" label. Perhaps before the English settlements of 1620- expanded trade from the region.
I suspect the turkey was quickly introduced as a domesticated bird in Europe shortly after contact with the Americas.
Otherwise, the turkey may be the closest cost-sensitive equivalent of whatever bird people at a lot of back then. Maybe it was a goose?