Not that I've heard of. It should be noted that while desks are an effective and commonly referenced "duck and cover" shelter device, "duck and cover" in general was more about the action of getting down and covering your head than being under a desk per se. As the film Duck and Cover makes clear, it was a strategy that could be deployed anywhere. And if one had adequate warning, you'd want to go a shelter more dedicated than a classroom. I've never seen anything that suggested desks ought to be changed for this reason, though. But I admit I have never seen anything about the history of classroom desk design (which, despite its seemingly silly scope, could actually be interesting — I have seen a great talk about the history of chalk boards, for example).

More broadly, there were infrastructure changes inspired by fears of nuclear attack, ranging from the Fallout Shelter Survey that resulted in the once-ubiquitous "fallout shelter" signs being posted in the 1960s, but also to the more unusual such as underground "shelter schools" like the famous Abo Elementary School in Artesia, New Mexico, which was constructed entirely underground.

Anyway, two useful resources for further investigation are Kenneth Rose, One Nation Underground: The Fallout Shelter in American Culture, which is a more historically-oriented monograph, but also David Monteyne, Fallout Shelter: Designing for Civil Defense in the Cold War, which is a more architectural approach (with some amazing visualss).