Hi, Jexie-
The theme is repeated several times during the movie, and there are variations. The final "Army" verse isn't on the Ann-Margret single. Her lyrics are just about what's posted above, without that final verse.
The Ann-Margret recording is introduced by this verse:

We love you Conrad, oh yes, we do
We love you Conrad, and we'll be true.

There was a similar verse about the Beatles. Bye Bye Birdie is a 1960 stage musical with a book by Michael Stewart, lyrics by Lee Adams, and music by Charles Strouse. The Beatles were formed in 1960, so I'm guessing the "Conrad" verse came first.
-Joe-