Nope.
The anti-nuke people took the song as their own, all right, but in 1955 the fourth member of the club was still five years in the future and the only "proliferation" which had occurred was the Soviet bomb in 1949 which led Julius and Ethel Rosenbergs' execution in 1953.
Pete and the rest of the "Where Have all the Flowers Gone" singers certainly didn't object to proliferation as long as the Soviets were the ones doing the proliferating.
Fun fact: "Where Have All the Flowers Gone" was included on Bernie Sanders's debut album "We Shall Overcome", released on cassette in 1987 before he departed for his honeymoon in the Soviet Union, which at the time had only four years to live.
Proliferation.
Here’s the definition, I think you have the word confused with something else.
It means the rapid increase and that’s what the song was about the rapid growth of the nuclear arsenal’s of major players in the world at that time
1 : to grow by rapid production of new parts, cells, buds, or offspring. 2 : to increase in number as if by proliferating : multiply. transitive verb. 1 : to cause to grow by proliferating.