I once spent a couple of years reading many, many American memoirs of World War I, both books and magazine articles.

There were plenty of references to drill sergeants chanting "hup, two, three, four" (and phonetic variants), and to troops singing both polite and bawdy songs on the march, but not one example of the modern "Sound off!"

That routine, however, was certainly popular in World War II, possibly only after the 1944 appearance at Ft. Slocum, N.Y., of Pvt. Willie Duckworth's "Duckworth Chant," in which the syncopated sound-off countdown figures prominently.

A 1945 recording: https://www.youtube.com/watch?v=Q6bhv4i8qso

The 1952 movie "What Price Glory" has World War I marines doing something similar. But they *don't* do it in the 1924 Broadway play that the movie's based on.