Hi Peter
If you are able to store the profile graphic on a publicly available address such as Google drive and paste the url into the notification editor the image will be embedded in the notification without login
For example
https://totara.img.email/images/632035868a1ec.png
This is OK for one file but the user profile pictures are stored in Totara which requires login
There is a way to bulk upload profiles into Totara https://totara.help/docs/upload-a-user-picture but you are wanting it the other way around. I am not sure how the public image url can be added in bulk.
regards