The short answer is no, it doesn’t. This simply means that the ingredients used in the product’s formula were grown according to the principles of organic farming, that is, with no harsh chemicals as pesticides and fertilizers. Besides, organically grown produce cannot be genetically modified.
There are other implications that come with this term, such as responsible sourcing, but this doesn’t guarantee good quality. Most products labelled organic are only partly so. It also doesn’t prevent the formula from being ineffective or imbalanced.