I doub t it,
Andy.
My references point Karine (KAPINH), meaning "woman from Karia," and used to signify "professional wailer" at funerals - nothing witty about that.
Also there is "Karinos" , the month of November in the Eastern Rolam (Byzantine) Empire - again unrelated.
Maybe there is some oblique connection with the word
Charis meaning grrace, but I doubt it.