Yes, there is a Yaphank As a twenty-year resident of Yaphank, New York, which is on Long Island about 60 miles east of Manhattan, I've learned some of the background of this movie.
Irving Berlin wrote "Yip, Yip, Yaphank" while stationed at Camp Upton in Yaphank during WW I. (Camp Upton is now the Brookhaven National Laboratory.) For this show, which was indeed written to be performed by the soldiers, Berlin wrote "Oh, How I Hate to Get Up in the Morning" and the melody of "God Bless America," which was actually cut from the show in its original form.
The show even ran briefly on Broadway in 1918 with a Camp Upton cast, according to the Internet Broadway Data Base.
After the war ended, the songs were put away, then brought out for the morale-boosting efforts of WW II. Berlin frequently rewrote and reused his songs; he revised the lyrics of "God Bless America" for Kate Smith and the rest, as they say, is history.