Are you using a test company or a test instance of SQL? Or do you have a completely separate test server?
When you run an upgrade, GP Utilities will upgrade all company db's and the Dynamics Db found on the one instance of SQL. If you are using a separate instance of SQL or a completely separate installation on a different server, you are correct.
For you sanity, back up EVERYTHING
BTW, when it comes to training users on 2013, get a copy of our book GP Version 2013 Unleashed. Visit our web site.