When I run the WUD container with WATCHATSTART=False and launch the web UI, I don't see any containers listed there.

I've not tested it further but most probably the containers are fetched/refreshed when WUD is going to check for the new versions. This makes sense from a WATCHER perspective, but from GUI point of view, the containers should be fetched at startup (or at least when the GUI is launched for the first time and there are no containers info yet) and shown there even if there are no watchers scheduled at WUD startup.