Yes, It is possible to check and export the Last Run Date of the report - 

  • Go to Metadata Search App
  • Search your report using the Search Box
  • Then go to the Report session OR you can use the Report toggle Option just on the records toggle and then search
  • Now click on the download button you can download PDF and CSV files
  • Your downloaded CSV file will look like the below image
  • Your downloaded PDF file will look like the below image