A test as shown that moving a message to another category sends the same notifications as posting a new message.
David Straub has confirmed that his preferences are set to only notify on postings to the GrampsWeb category. A message was posted to Help but was specific to GrampsWeb. I moved the message without adding an @ flag to notify his account then made a followup inquiry by Private Messaging.
David confirmed that Discourse sent him a Notification the same as if it had originally been created in his Category.