Yes, you can see the status of uploaded files.
When the toggle is OFF - You can see if the files are uploaded or not in the status column.
When the toggle is ON - After uploading the file, the success status comes to state that your files are uploaded successfully. 
PS: View Mass File Upload, Salesforce file upload app on Salesforce AppExchange: https://appexchange.salesforce.com/appxListingDetail?listingId=82cf236b-1ee8-4ea7-aebf-fd0c89fb93bd