Miller's situation is a little more nuanced - he was crew on an Allied Bomber that levelled the Benedictine monastery at Monte Cassino in Italy during World War I, falsely believing it was occupied by German troops. His subsequent PTSD was a driving force behind his subsequent conversion to Roman Catholicism, and he uniquely imbues the novel with the structure and lexicography of a closed order. His fear was not so much war - atomic or otherwise - as it was the loss of knowledge and tolerance as a consequence of the cyclical and barbaric nature of human society.
Indeed he takes some other significant cues from Bradbury - who faced a similar, if less poignant, Road to Damascus moment upon learning about the destruction of the Library of Alexandria.
For example, the concept of 'Booklegging' is lifted wholesale from Fahrenheit 451, published a few years prior. Bradbury has oft-cited political correctness as an allegory for the censorship in the book, and Miller makes his views very clear by the time we encounter the flanderised Atheist in the final third of Canticle - reinforcing his core theme of the juxtaposition of scientific progress and moral wisdom, and the shared thematic motif expressed by Montag in Fahrenheit 451 that the books of the past have messages that can save society from its own destruction.
As such, it is clear to me that the fear of war - and the trendy nihilism imbued by the then innovative atomic variant - doesn't so much affect mid-century fiction as the cultural and societal upheaval seen as the Baby Boomers assumed their place as the generation in ascension. In many ways this echoed the post-WW1 Brideshead Revisted era of England, merely substituting a surplus of capital for a dearth of inheritors.
Thus, while both can be read as atomic jeremiads, they are more appropriately realised as treatises to the social and political mores at the time. The scare for the average American wasn't so much Nuclear as it was 'Red' - something that can be seen in the stubborn cargo-culting of very American Institutions and Practices in the post-apocalyptic canon. As can be seen across the US Sci-Fi Canon, preservation of self is often secondary to the preservation of American Exceptionalism; be it via an ICBM or the stochastic terrorism of McCarthy.