The more I think about it, the more I'm in "not propaganda" camp.

Here's my reasoning. Imagine you're a government (and temporarily excuse my composition fallacy). If you know there is a high probability of nuclear war, you need to figure out how your country is going to survive it. Whether you're a benevolent government or not, the way you educate your public is going to have a real impact on how well your country survives the war. So you take stock of certain facts:

1. People too close to the blast will all die, and no amount of public awareness will change that.
2. People downwind of the blast but far enough away to survive the actual explosion will all die if they don't get underground.
3. People upwind of the blast but far enough away to survive the actual explosion will be horribly burned and all die if they stand there like dopes looking at the explosion. However, if they can get some concrete between them and the blast and stay there for a little while, they'll survive without any adverse effects.

It seems to me that "duck and cover" is really meaningfully helpful for the 3rd point. The details of how people respond to a bomb going off really really matter for anybody who's outside the immediate blast area, and if you can educate your people on the right way to respond, you'll save many more people. This film, silly as it is (a newspaper is probably not the best radiation shield), does actually provide meaningful ways to survive certain aspects of a nuclear blast.