They did dozens of tests of the Minuteman missiles and reentry vehicles. The warheads were tested underground until the comprehensive test ban treaty of 1996. So it's pretty likely that the systems would work if needed. One risk is that something may have gone wrong with the warheads over 30 years. (Of course they maintain them, but without testing you can't be sure.) Another risk is that you don't know how the missiles would function in an environment with nuclear blasts and EMP all over the place. They put a whole lot of effort into mitigating these factors, but you can't be sure. Hopefully we never find out.