In any case, no, this isn't a problem with the watch's Cellular service. It's an existing issue that's just suddenly become extremely relevant.
Glad to see that it is very likely going to be solved in short order. My bet is that there are a few people at Apple that are going to pull a few all-nighters to get an update to us by next week. We'll see if I'm right.
That being said, my iPhones have all had a similar problem. If Wifi signal is weak, or is fully connected but there is no connection to the Internet through that network, then it does a terrible job switching to LTE. Perhaps this is more a bug in how Apple handles this on all of their devices. Maybe now it will get some attention.