Yoko, if the teacher who set the quiz left the default settings on the (which most do), then, yes, it should automatically save what you have done when the time runs out.
Quiz
Already answered essay but time ran out, are my answers saved?
ការពិភាក្សាត្រូវបានបិទ ដូច្នេះអ្នកមិនអាចឆ្លើយតបទៀតទេ។