I've created a ticket and added the relevant information to it. Just adding this here in case someone else has more information to contribute (experience from other android devices etc).
Further testing has revealed that it appear to be more of a problem with alternate locations for file-storage than with synchronisation itself. I can not get Bandhelper to use any folder other than the default for file storage on any Android-device (have not tested on iOS). It should be as simple as pointing Bandhelper to an empty directory and tap "download missing files" in settings. With an empty directory for storage Bandhelper indicate that files are missing in recordings and documents, but nothing happens when I hit "download missing files". The client does not even attempt to connect to the server for download. The client will OTOH download (repeatedly and eventually crash), but fail to save, additional files during synchronisation should someone add a new file on the server while the client is set to use an alternate folder for files.