Due date and appointment date is not related. Legally speaking you will not be allowed to drive after 9-23, so you need to go to DMV as drop in appointment before that day to ensure you're allowed to drive after the expiration date. Be prepared to wait in long line though
You can definitely go and get this all done before your schedule appt. As long as your willing to come early and wait in line. Just be sure to bring EVERYTHING you need, they won't let you in the office otherwise.
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