There's an episode of Boardwalk empire where Nucky makes a joke about Jimmy fighting World War 1 "to make the world safe for democracy". in 1920 would anybody have been using that kind of language with regard to America’s involvement in the War?

I assume you realize that that exact phrase was used by Woodrow Wilson in his address to Congress on War. It had definitely entered the popular vocabulary, and was used in popular appeals, such as Bryan's 1920 "Dry Plank" speech to the Democratiic National Convention; conversely (I am not sure whether directly linking to the NYT archive works...) here is an article disappointed that after fighting "to make a sick world safe for democracy", Prohibition is the law of the land.