Yes. Human reliability was considered a key aspect of deterrence theory. In the US this was especially stressed, and any indication that one might not carry out the orders would lead to one not being assigned to nuclear duties. (The case of Harold Hering is instructive on this — in the 1970s, he asked, while being trained to be a missile commander, how he would know if an order from the President was sane or not, and he was discharged as a result.) Repeated drilling and use of checklists, which reduced opportunities for consideration of the consequences or any kind of moral objections, were extensively used in the US. If anything, the soldiers assigned were probably too gung ho about the whole thing — there are indications that in the 1950s there were many who would have possibly started a nuclear attack without an official order if they thought general war had been declared.

Schlosser's Command and Control and Ellsberg's The Doomsday Machine are two popular accounts of these kinds of activities. You can also check out the Radiolab podcast "Nukes" which talks both to a nuclear weaponeer and to the aforementioned Harold Hering. (And to me, as well!)