I guess it will not work. Most data records in the database have server_id columns and the server_id is unique in the cluster. A single server has server_id 1 for all records and the controlpanel server on a multi server setup has server_id 1 too, so when you copy the database from one server to another, it will stay a single server setup that runs controlpanel and sites on the same system. So if you would want to do that, you will have to edit records in the database.
My recommendation is to add a second server as slave to your current server, so the current server will stay the master. Then you can add new sitees from the controlpanel of the first server on the second server or you migrate some of the largest sites to the new server if the load on the old one gets too high.