Yes, you can see your total records and files count on the Mass File Download Tab. You can see the files on any tab inside the Mass File Download tab (Related Files, Static Resources, Documents, Files).

Go to the Mass File Download tab, 

  1. Select an object.
  1. Choose a ListView (if the Show List Views toggle is set to "ON") or Search for a record (if the Show List Views toggle is "OFF").
  1. Select a filter for related files and attachments (optional).
  1. Click the Search button.

You will be displayed with the Files Count with Parenthesis in blue color

EG: Related Files & Attachments (3433).

Under that, you will see the number of records having that many files.

Showing (3433) Files & Attachments of (14) Account records.