MySQL master/slave database replication?
No, Drupal doesn't.

Master/Slave replication is the job of the database management system, not Drupal's. All that Drupal does is use it, by using the slave server for specifically marked queries.

To be able to use replication, you either need a pre-configured hosting environment which already provides this or full access to the database server so that you can configure it. Replication happens on a server to server level, not database to database. In short, Pagodabox will most likely not allow you to set up replication.