This claim is not well-sourced (i.e. I exaggerated way beyond what we can prove is true.). Michael Balfour's 1979 book "Propaganda in War 1939–1945: Organizations, Policies and Public in Britain and Germany" discusses the slogan briefly in a footnote saying that it was considered too extreme vs. other possible slogans:

""By 3 August they had drawn up a shortlist of five slogans which was shown on that day to Hoare, who chose the three actually put into production (INF 720). The third poster 'Keep Calm and Carry on' [sic] was never displayed, as too obviously inappropriate to the actual conditions.""

  | I don't even know if it makes sense to print
  | a propaganda poster for use after occupation.

My thoughts as well. I'm pretty sure that the Nazis would do just fine generating their own propaganda posters had they occupied Britain.