The Persistent Chat Server role is optional, and not all deployments include this role. If the role is not implemented, there is really nothing to worry about here.
In the event that the Persistent Chat Server role is deployed, it could be on a separate pool and have a different set of databases than the rest of the Lync deployment. This will vary between the Standard Edition (collocated) and Enterprise Edition deployments. The backup and restore is done with their own set of backup commands and must be performed using PowerShell.
The Persistent Chat database and information is not included in the Export-CsConfiguration or Get-CsTopology command (except for the name of the pools, database, and core information).