Logically speaking,
The universe doesn't care about time nor is it concerned about measuring it. It simply is time and the only creature created that cares about measuring time is humans. Why? I don't know. However, a self replicating watch is in my expert opinion, outlandish, absurd and ridiculous.
Logically speaking,
If a self-replicating watch was a thing that was a natural creation then it would have already been here thus we would never have had a need for a regular watch to begin with. Of all the discoveries we've made and inventions we've created, in 2018 we haven't found a " self-replicating watch " yet? It's because such a thing would indeed need to be created and molded to the understanding of a human's brain. You would have to consider if this technology is indeed a natural creation then you will undoubtedly have to consider the fact that animals are using this " time piece " as well to navigate. They too are a part of nature yet there are no studies or discoveries about animals of any kind, including insects, functioning off the awareness of some sort of self replicating watch.