I was tempted to use this feature, but wasn’t sure about the deadline either. Students might have approved extensions and even if they don’t - my university’s regulations allow students to submit late, but a penalty will be applied to late submission (which is the minimum pass mark).
I just tried the deadline with a test student account.
When changing files on the GitHub web interface I did not get a message telling me that the deadline has passed (which is fine, as a student might have an extension, so the deadline might not apply).
In the ‘classroom’ I saw the latest version, which was (in this case) submitted after the deadline. If you hover with your mouse over the “submitted x minutes ago” you get the exact time of submission, so it would be possible to see which commit was done before the deadline and which one was done after, even if there were many around the time of the deadline.