Hi,
No, if there is no network connection between Orthanc and the Storage, Orthanc will simply fail to write the file and report the errors accordingly through the DICOM protocol or the Rest API HTTP status code.
Activating the HybridMode would not help to handle these network connectivity issues unless you configure the HybridMode to WriteToFileSystem and move files to the object storage through the API. Note however that this scenario was not tested.
Best regards,
Alain.