Does FlexiCapture have an approach to enable/disable the automatic export for the whole project?
There is no possibility in FlexiCapture to disable or enable export on the project level. However, if the Advanced Workflow is used, it is possible to restrict entry conditions for the export stage. Thus, if the document satisfies some conditions – it will be exported. And wise-versa, if conditions aren't satisfied – batch will be routed to another stage: https://help.abbyy.com/en-us/flexicapture/12/distributed_administrator/rule_settings/
Each batch type has its own workflow setting. It is required to set entry conditions for each batch type.