Great question! I had not done this before but had a tinker to see what is possible and I do think it is with a caveat on usability.
I created a quiz with a single attempt and three questions (as a trial). Each time as the student account I answered a question, Canvas auto-saved the quiz response. If I navigate away (and click yes to the prompt that I am navigating away from the quiz), it gives me the ability (as a student) to resume the quiz.
A couple of things, this may not be the best user experience for you or the students. For you, you won't get a submitted result until the students actually press the submit button, additionally, if the students press submit early (rather than just navigating away) they may submit prematurely, and have only completed half the quiz.
It does (however) seem doable. Another thought that came to mind would be to do a several quizzes that are broken up into a logical set. That would mean the students complete the separate quizzes bit by bit and you get to see progress as they go, however, I can see that this would make the grade book a little complex (musing out loud).
Hope that helps! Please let us know how you go with it!