Ok, I gave it a try.
When the site switches to maintenance while you're in a quiz attempt and you press submit, you're taken to the maintenance notification (as expected). If you go back to the previous page via browser arrow you can, or rather have to, retake the quiz. The timer and previously entered answers are reset.
If the site goes out of maintenance and you refresh while you're on the maintenance notification page, you're taken to the quiz review page (where you would have ended up without maintenance mode), but the timer keeps running in the meantime.
So if you only have one page in your quiz (page breaks result in the maintenance notification) and your quiz is set to auto-submit when the timer has run out, it's not a big problem.. but it's probably a good idea to add an explanation/instructions to the M-mode-notification, like..
"if you were in a quiz attempt and came to this page when you tried to submit: your progress has been saved and will be auto-submitted when the timer runs out, you may now close this tab or refresh it later..." or something like that, just to make sure people don't panic.
regards,
Seb