It is possible to "Export" all data from all documents and/ or signers from the "My Documents" page.
However, it is not possible to "bulk download" all of the final PDF's.
Although, you can set up a direct integration to Google Drive or Dropbox. With this integration, all signed documents will automatically be uploaded into a Google Drive or Dropbox folder.
After setting this integration up, this will be an automatic upload of all signed documents and signing logs from that point forward.
Have a look at the following SignRequest integrations: https://signrequest.com/en/integrations/
Just let me know if you have any additional questions.