The issue of comparison is exactly why this is all interesting, though! If NIST completely loses the clocks at Boulder, they will need to 'restart' them later by synchronizing them to some other standard like another NIST site or the Navy. The physical distance between locations and means of comparing their time signals makes this a tricky process, and one that I don't think the Boulder clocks have ever been through before.
The gold standard used to be to literally "ship" the time reference, by flying a portable atomic clock between sites. I know that NIST has fiber lines between sites and metrology has continued to advance, my impression is that you can now get more accurate results by sending signals over precisely measured fiber. But if NIST does end up in that scenario I'm sure we'll get a paper about how exactly they end up handling it.