Yes. For items to be migrated between Source and Destination Public Folders, the types of the folders must be correct. This means that when migrating email, both the Source and Destination must be set up as email folders. The same holds true for calendars, contacts, tasks, and most other item types.
However, when creating new Public Folders through the Exchange Admin Center, they are always created as email folders. This means that if you create a folder at the Destination that has the same name as the Source, and the Source folder is not an email folder, then no data will be transferred between the Source and the Destination.
We detect this condition and throw an error stating: "Source folder type does not match Destination folder type."
If you see this error, it is likely that you have created your Public Folder with the incorrect type (e.g., it was created as an email folder when it should be a calendar folder or contact folder).
In order to fix this error, you have to either delete the existing folder at the Destination and allow the migration process to create the folder, or you have to create the folder as the expected type. This can currently only be done through OWA or Outlook, and not within the Exchange Admin Center or through PowerShell.