No. Carbons are only doing this:
User 1 sends a message to user 2 in Conversations. This same message is showing as sent in Gajim also (in its history, in the chat window).
You probably want to sync received messages also (or only), but there is currently no working solution. There is a system property route.all-resources , but it only works when sending messages to bare JID and most clients use full JID to send subsequent messages (Re: [3.8.2] route.all-resources doesn't work? ).
Unless someone creates a plugin or something modifying the route.all behavior nothing can be done to sync incoming messages to all connected resources.