It doesn't seem likely. Effie I. Crockett was descended from a Maine family that traces its ancestry to [[Crockett-35 | Thomas Crockett]], a native of Devon. England who emigrated ca. 1630, and died in Kittery, Maine.
Davy Crockett traces his ancestry to [[Crockett-590 | Joseph Louis Crockett]], a native of Cork, Ireland who died in Roanoke, Virginia.