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.
Note: While none of the Annex 2 countries that are signatories have conducted tests since 1996; the treaty never took effect because it was never ratified by all the required countries. Most notably the US, China, and Russia (although all three signed). In 2023 Russia officially withdrew, allegedly based on the US non-ratification. At least one political candidate for the presidency in the US has advocated for resuming testing. It is not inconceivable that testing could resume in the near future.
Opinion: I don't think the US would if Russia or China didn't first. China likely won't for the same reason the US doesn't need to: they have super-computers and the sims line up with the data from prior tests. Russia might however if only to saber rattle, although they likely don't need to either. Russia however is likely not in any hurry to have a test failure right now. So while testing could resume, I wouldn't put money on it.
