the message you get during the object list check is releated to the Add-On deletion/uninstallation. It means that for now there is no handling defined for the Logical database object during the deletion/uninstallation. This check is only relevant in case you would like to define your Add-On as deletable after installation.
Choosing "Set Entries to Completed" should keep the logical DB-objects on the piecelist.
If this is not the case, please open a ticket with SAP support under XX-PROJ-AAK. Important would be that a remote connection to the system exists so SAP support could logon and investigate.