The connection is strong but the promise unfulfilled is horrific, as this superb article by Prof. Roberto de Mattei from Rorate-Caeli relates:
Since this year is the centenary of the Apparitions of Fatima, let us consider this point only. When Vatican II opened in October 1962, Catholics from all over the world were waiting for the disclosing of the Third Secret and the Consecration of Russia to the Immaculate heart of Mary. John Haffert’s Blue Army led a mass campaign for years in this regard.
What better occasion for John XXIII ( died 3rd June 1963), Paul VI and with circa 3000 bishops gathered around them, in the very heart of Christendom, to meet Our Lady’s requests in a solemn and unanimous way? On February 3rd 1964, Monsignor Geraldo de Proença Sigaud, personally delivered to Paul VI, a petition signed by 510 prelates from 78 countries, which implored the Pontiff, in union with all the bishops, to consecrate the world and in an explicit manner, Russia, to the Immaculate Heart of Mary. The Pope and most of the Council Fathers ignored the appeal.
If the Consecration request had been done, great graces would have poured down on humanity. A movement of a return to the natural and Christian law would have begun. Communism would have fallen many years earlier, in an non-fictitious way, but authentic and real. Russia would have converted and the world would have experienced an age of peace and order. Our Lady had promised this.
The failed consecration allowed Russia to continue spreading its errors throughout the world and these errors conquered the highest ranks of the Church, inviting a terrible chastisement for all of humanity. Paul VI and the majority of the Council Fathers assumed a historical responsibility for which today we gauge the consequences.