Hi, Joel! Setting a due date will not stop a student from submitting an assignment late. Canvas will mark the late submission as late though, and of course, you will see the time stamp to show you when the student did submit the assignment. If you want to allow late submissions for a specific window, you can set an Available until date:
In the screenshot, the assignment is due on March 18, but students can submit late assignments until March 21. If no "until" date is set, students will always be able to submit -- at least until the term ends.
I hope that helps!