There was another movie from that era that made fun of the Soviet Commies. No Greta Garbo, but another top notch exotic actress (Hedy Lamarr?). All I remember is they somehow wound in a tank and accidentally went over the border into Romania or some other small country, convincing them they were being invaded. It was also a light comedy.
Sounds like that movie with Bill Murray and the RV (Stripes) might have taken that earlier idea?