At the moment, no — threads are set to Tracking (not Watching) when they are started from a chat you’ve sent (i.e. the thread OP) and when you reply to a thread.
We debated this when building Watching, but weren’t sure if folks would want that or not since the Watching notifications are more aggressive. However, we’d love to hear feedback from anyone who would find that helpful so we can consider it for a future improvement!