We've set up Alfresco to use the MySQL database; however, we're not sure it's using that instead of the Hibernate database. Is there a table I can look at in MySQL that would indicate recent activity such as adding content/groups/spaces, so I would know we're actually hitting the MySQL database?
HIbernate is not a database. Hibernate is the persistence layer that communicates with a database, in your case, MySQL. If you're able to start up Alfresco, you are most likely communicating with MySQL unless you configured your instance of Alfresco to use Derby. This doesn't seem to be the case, so it's communicating with MySQL.