They may be certified to some maximum error, but you still need to test them to find out what the actual error of your particular watch is (I'm calling it a "watch" here for simplicity, "chronometer" would be more technically correct).

In order to test your watch, you need a known time source, which would be missing after a grand disaster. So hopefully you tested and documented your watches error rate BEFORE the disaster. But even if you had a good watch, with a previously tested and documented error rate, you could only use that to adjust your calculations for so long. Eventually you would want to reset your watch to the known time standard again. But the known time standard is still unavailable, due to the disaster. A good watch would certainly serve you better than an el-cheapo non-certified one. But it would only serve you for so long, not indefinitely.

This is the gist of my concern in labeling CelNav "a backup for when everything has gone to heck". That may be true, as long as "everything" does not include a good time standard to reset your watch to. CelNav would be good for a while, but you would eventually need a known time standard, or a known location to reset your watch from. You would also need an almanac that contains data for a very long time. Or be a math whiz in spherical trigonometry (which most people have never even heard of) to calculate everything from scratch. The current "Long Term Almanac" goes to year 2050. Enough to cover my lifetime, but not my kids.

Long Term Almanac