I'm not sure if this is a bug or not but if you create a Quiz whose quiz_type is assignment and then edit the associated Assignment and set its grading_type to not_graded then it breaks the association between the Quiz and the Assignment. Not only is the association broken but a new Assignment is created. I'm not sure if this is the intended behavior or not but I thought I would bring it up because it was incredibly unexpected and I couldn't find any documentation on this. I was accessing the API through this Python wrapper if it makes any difference.
If you want the background on why I didn't just make the Quiz a Practice Quiz or Ungraded Survey instead of making it an Assignment Quiz, it is because the API only has support for differentiated assignments (assignments assigned to a subset of the class or assignments where students have different due dates) for Assignments and not Quizzes. I think this is kind of weird because you can differentiate NonAssignment Quizzes through the web browser but not through the API (or at least I haven't been able to figure out how).