Does a character with no account count as a pack member?

No, unfortunately, this would not be allowed. In order for a puppy, or any NPC named character, to exist in the game world, they require an account. For pack characters, they also need to be ranked as an NPC for visibility. This is admittedly not super clear in our NPC Guidelines, but has been the case for a little while now, so I'll add clarification to that Help Doc!