Hi,
Yes it’s possible!
Implementation
You’ll need to have the custom icons (you probably want to have them cropped to the right dimensions beforehand) uploaded to a Media Set with legible file names.
You will then want to implement pipeline logic to join the correct media reference to the correct row(s) in your backing dataset.
When you create the object type, you’ll have to add hubble : icon as a type class to the Media Reference property.

