You asked two questions here:
"Can we create an assignment that's completely unlinked from the gradebook?"
Any Assignment can be excluded from the Gradebook, so it Don's have to affect your course Grades
See this page as your starting point: https://docs.moodle.org/36/en/Grades_FAQ
Look for "How can I grade some of my activities without the results affecting my students' course total?" section.
"...can we post a feedback document without the student having to take any action first?"
Good question, and I'm not sure, because I've never tried that!
Usually a learner would submit something, and a teacher would attach a feedback file.
So I think you should just setup an Assignment and test who you want to do, to see if it can be done?