You have asked about whether nuclear devastation on this planet would effect the Sankirtana Movement .
No, there is nothing that can stop the Sankirtana Movement because it is the will of God Himself, Lord Caitanya, that His Holy Name be heard in every town and village.
Neither can the demons devastate this planet independent of the will of Krsna. Nothing happens without His sanction. If Krsna wants to kill someone no one can save Him, and if Krsna wants to save someone no one can kill him. For our parts we should just be determined to carry out our mission against all opposition, demons, nuclear war, whatever. The whole universe is finally subject to certain annihilation by the will of Krsna, but devotional service is eternal and is the only certain way one can save himself from devastation. (S.P. Letter to: Makhanlal Mayapur 22 June, 1973)
“This prediction of Lord Caitanya Mahaprabhu’s is now actually coming to pass. The Krsna consciousness movement is being distributed all over the world through the chanting of the holy name of the Lord, the Hare Krsna maha-mantra, and people who were leading confused, chaotic lives are now feeling transcendental happiness. They are finding peace in sankirtana, and therefore they are acknowledging the supreme benefit of this movement. This is the blessing of Lord Caitanya Mahaprabhu. His prediction is now factually being fulfilled, and those who are sober and conscientious are appreciating the value of this great movement.” (Caitanya-caritamrta, Adi lila 9:40)
“As stated in the Srimad-Bhagavatam, the incarnation in the Age of Kali is Lord Caitanya Mahaprabhu, who spread the worship of Krsna by the sankirtana movement (congregational chanting of the holy names) and spread Krsna consciousness throughout India. He predicted that this culture of sankirtana would be broadcast all over the world, from town to town and village to village.
Lord Caitanya as the incarnation of Krsna, the Personality of Godhead, is described secretly but not directly in the confidential parts of the revealed scriptures, such as the Upanisads, Mahabharata, Bhagavatam, etc. The devotees of Lord Krsna are much attracted by the sankirtana movement of Lord Caitanya. This avatara of the Lord does not kill the miscreants, but delivers them by His causeless mercy.” (Bhagavad-gita 4:8 Purport)
“Sankirtana means chanting of the holy name of the Lord. The Hare Krsna movement is not a new movement as people sometimes mistakenly think. The Hare Krsna movement is present in every millennium of Lord Brahma’s life, and the holy name is chanted in all the higher planetary systems…. The sankirtana movement that was started in this world five hundred years ago by Sri Caitanya Mahaprabhu is therefore not a new movement. Sometimes, because of our bad luck, this movement is stopped, but Sri Caitanya Mahaprabhu and His servants again start the movement for the benefit of the entire word or, indeed, the entire universe.” (Srimad-Bhagavatam 7:15:71 Purport)
Lord Chaitanya the incarnation of the Supreme Personality of Godhead Sri Krishna
Lord Chaitanya Mahaprabhu (1486-1535) is the most recent incarnation of the Supreme Personality of Godhead Sri Krishna. He appeared 500 years ago in Navadvip, West-Bengal and started His worldwide Sankirtan mission of propagating the chanting of the holy name of the Lord (the process of self-realization for this age – to meditate upon the sound of the maha-mantra: Hare Krishna Hare Krishna, Krishna Krishna Hare Hare, Hare Rama Hare Rama, Rama Rama Hare Hare ). He left us only eight verses, called Siksastakam , in which His mission and precepts are revealed.
Lord Caitanya is Lord Krishna’s devotional form and is mentioned in Srimad Bhagavatam 11.5.29 “In this age of Kali, people who are endowed with sufficient intelligence will worship the Lord, who is accompanied by His associates, by performance of sankirtana-yajna”, (chanting the Maha Mantra). Lord Sri Caitanya Mahaprabhu is Lord Krishna’s most merciful form who comes under the guise of a devotee. Lord Sri Caitanya Mahaprabhu was setting the perfect example of the “pure devotee of God”, yet, He is God Himself! He is the devotional form of Lord Sri Krishna. The purpose of Lord Caitanya’s appearance was to spread the sankirtan movement of chanting the holy names of the Lord to every town and village worldwide as the main means of God realization for this present age of Kali Yuga. He encouraged His followers to write books on Vaishnava sastra and to defeat the present infection of mayavadi impersonalism that is present everywhere and establish within the hearts of all, the practice of bhakti (love and devotion) to the Supreme Personality of Godhead, Lord Sri Krishna.
Commentary by A. C. Bhaktivedanta Swami Prabhupada
Lord Chaitanya Mahaprabhu recommended: ceto-darpana-marjanam. Marjanam means “cleanse,” and darpanam means “mirror.” The heart is a mirror. It is like a camera. Just as a camera takes all kinds of pictures of days and nights, so also our heart takes pictures and keeps them in an unconscious state [Subconsciousness]. Psychologists know this. The heart takes so many pictures, and therefore it becomes covered. We do not know when it has begun, but it is a fact that because there is material contact, our real identity is covered. Therefore ceto-darpana-marjanam: one has to cleanse his heart. (SP: Science of Selfrealization)
And when the heart is cleansed, then a person becomes eligible for being freed from the clutches of maya, or the materialistic way of life. He understands that he is not this body-that he’s a spirit soul, and that his business is therefore different from merely material concerns. He thinks, “Now I am engaged only in seeking these bodily comforts of life. These are not at all essential, because my body will change. Today, since I am in an American body, I think I have so many duties as an American man. Tomorrow I may be in an American dog body, and immediately my duty would change. So I can understand that these bodily concerns are not my real business. My real business is how to elevate myself-as a spirit soul-to the spiritual world, back to home, back to Godhead.”
When the mind is completely washed of all material contamination, the pure consciousness acts. The sound vibration from the spiritual sky can automatically cleanse all material contaminations, as confirmed by Chaitanya Mahaprabhu: ceto-darpanam-marjanam [Cc. Antya 20.12]. We need only take the advice of Lord Chaitanya Mahaprabhu and chant the Hare Krishna mantra to cleanse the mind of all material contamination, and this may be considered the summary of this difficult verse. As soon as the whole material contamination is washed away by this process of chanting, all desires and reactions to material activities become immediately vanquished, and real life, peaceful existence, begins. In this age of Kali it is very difficult to adopt the yogic process mentioned in this verse.
Unless one is very expert in such yoga, the best course is to adopt the ways and means of Lord Chaitanya Mahaprabhu, Sri-Krishna-sankirtanam. Thus one can gloriously become freed from all material contamination by the simple process of chanting Hare Krishna, Hare Krishna, Krishna Krishna, Hare Hare / Hare Rama, Hare Rama, Rama Rama, Hare Hare. Just as life in this material world has its beginning in material sound, similarly a spiritual life has its beginning in this spiritual sound vibration. (SB 4.23.17 pp)
In His Siksastaka, Lord Chaitanya describes the progressive benefits of chanting Hare Krishna. First, ceto-darpana-marjanam [Cc. Antya 20.12]. The beginning is cleansing the heart, because we are impure on account of dirty things within our heart, accumulated lifetime after lifetime in the animalistic way of life. So everything-advancement of spiritual life, culture, tapasya-is meant to cleanse the heart. And in this process of chanting the maha-mantra, the first installment of benefit is the cleansing of the heart. Ceto-darpana-marjanam.
Specifically, chanting the Hare Krishna mantra purifies one, and this chanting is therefore recommended by Sri Chaitanya Mahaprabhu. Ceto-darpana-marjanam: [Cc. Antya 20.12] by chanting the names of Krishna, the mirror of the heart is cleansed, and the devotee loses interest in everything external. When one is influenced by the external energy of the Lord, his heart is impure. When one’s heart is not pure, he cannot see how things are related to the Supreme Personality of Godhead. Idam hi visvam bhagavan ivetarah (Bhag. 1.5.20). He whose heart is purified can see that the whole cosmic manifestation is but the Supreme Personality of Godhead, but he whose heart is contaminated sees things differently. Therefore by sat-sanga, or association with devotees, one becomes perfectly pure in heart. (SB 4.24.59 pp)
In this way the person who chants Hare Krishna purifies his consciousness. Then his materialistic activity is stopped. He knows, “This is simply a waste of time. I must act spiritually.” That is knowledge, which comes from cleansing the heart (ceto-darpana-marjanam [Cc. Antya 20.12]). The illusion of wrongly working on the basis of the bodily concept of life is overcome simply by the chanting of the Hare Krishna maha-mantra. This is the first installment of benefit from chanting. (SP: Civilization and Transcendence)