Luther’s Large Catechism clearly places sanctification under the second and third articles of the Creed, which it presents as a statement of the gospel, not the law. (It instead presents the law in terms of the Ten Commandments.) In excluding the law from sanctification, Luther faithfully followed St. Paul (Galatians 3).
To put it another way, the Spirit sanctifies and renews us through the gospel, not through any third use of the law. That does not deny the importance of the law in informing (third use), condemning, and compelling Christians who would otherwise sinfully follow man-made works as if they were good, as Article VI of the Formula of Concord says.
Does a lack of sanctification directly result from a denial of the third use of the law or from a lack of exhortations in sermons to obey the law? No, sanctification comes only by the gospel, not also by the law.
That said, the law in its second use does work sanctification indirectly by bringing about repentance, that is, by preparing the Christian to return to baptism (gospel). That is the entire Christian life, as Luther said: “a truly Christian life is nothing else than a daily baptism” (Large Catechism). In other words,
For what is our prayer but a confession that we neither have nor do what we ought and a plea for grace and a happy conscience? This kind of confession should and must take place incessantly as long as we live. For this is the essence of a genuinely Christian life, to acknowledge that we are sinners and to pray for grace. [Martin Luther, Preface to the Large Catechism, 1529 revised edition. Tappert, T. G. (2000, c1959). The Book of Concord: The Confessions of the Evangelical Lutheran Church. Philadelphia: Fortress Press.]