Based on our online documentation, the "Processed" stage means that processed documents are sent to this stage. More information about that you can find in this article:
It means, the batch can be moved to this stage either automatically or via the script (theoretically, it is possible even to bypass the export stage).
Of course, FlexiCapture 12 checks the integrity of the data being exported, and the export task is considered as a separate transaction: the export task is marked as successful only once it is fully completed.
Also, we have the IActionResult object that is available for the export script in the Document Definition. So, it is possible to control and double-check the behavior of IActionResult. Succeeded from there as well: https://help.abbyy.cn/en-us/flexicapture/12/developer/iactionresult.