No, it does not. If an ingredient is a low enough proportion, the product can be labeled as “free” of that ingredient. If you read the ingredients list, you may see that there are small amounts of the “free” ingredient.
Organic can be healthier if it is truly without chemicals, which our bodies do not want.
Always be sure to read the ingredients list to make the choice; and, better still, eat mostly fresh and natural foods that do not need a label or list.