It seems unlikely to me, but not impossible.
After Butler retired from the US Marine Corps in October 1931, he made a
nationwide tour in the early 1930s giving his speech "War is a Racket".
The speech was so well received that he wrote a longer version as a
short book published in 1935.
In 1938 when Rutherford came to England he organised a placard campaign preceding his lecture on "Face the Facts" at the Royal Albert Hall. In the biography of Albert Schroeder in The Watchtower, March 1, 1988, pp.10-17 Schroeder says (pp.13,14):
To advertise the public talk, sandwich-sign parades were organized. Before the first information march was due to take place, Brother Rutherford asked to see me. While we were discussing convention matters, he was doodling with his pen, which at times he did when talking with someone. He peeled from a pad what he had written and handed it to me. “What do you think of that?” he asked.
"RELIGION IS A SNARE AND A RACKET,” it read.
“It looks blazing hot,” I replied.
“I meant it to be strong,” he said. He then instructed that placards with this wording be made in time for our first convention information march Wednesday evening.