Yes, Mass File Download works for custom objects as well. 


All you have to do is:

  • Select the MASS FILE DOWNLOAD tab.
  • Choose custom object from the drop-down menu.
  • Select a search mode from the drop-down menu.
  • Click on the Search button.
  • All the related files and attachments will be displayed, from where you can download files and attachments as shown in the images below.