LOS ANGELES (TheWrap.com) – "American Idol" and "The Voice" might be rivals in the singing-competition arena, but the two shows will come together – sort of – for the Christmas season. "Voice" coach Cee Lo Green and Mariah Carey – who begins her stint as an "American Idol" judge when the show returns in January – will both be on hand to perform on NBC's 15th Annual "Christmas in Rockefeller Center," the annual celebration of the lighting of the Christmas tree in New York's Rockefeller Center. …