If this gets enough signatures, the EU will create a review committee, which, if they approve of the initiative, will draft a law for the European Parliament to vote on.

No, there's no way to automatically make something become law. A successful petition just forces the European Commission to discuss it and potentially propose legislation. Even though it's not forcing anything to happen, there is an incentive for the commission to seriously consider it as there is probably a political cost to officially denying a motion that has proven that it concerns a large amount of people.