Short answer: it depends. Judges are free to utilize whatever procedures they see fit, as long as they fit within the rules of practice that apply to that jurisdiction. In this case, a Judge could place a motion hearing on calendar based on the notice from your PO. In that case, your Public Defender would be there to close your case. Some Judges will not hear an issue unless prompted.
This is my advice. If a lot of time passes without any word from the court or your public defender, hire private counsel to file the motion. If you hired private counsel to file a motion, you will definitely get on calendar and the case will likely be closed. Be careful, because this is where people sometimes fall through the government cracks. It would be relatively inexpensive to hire private counsel to do this one motion.