Sorry, no. We currently have no means to script running searches and exporting their hits. We can schedule searches to run. That part is built into the product. The export is the part that can't currently be scripted. Such a capability would require an enhancement request.
FYI, the customer would have the potential to export more items than they would need in a litigation case if they just export without reviewing the search hits. I hope they are aware of this as they could save money by performing an internal review of the search hits and only export those that are relevent to the litigation or issue under investigation.
