Welcome to the QuickBooks Community, Porterboys. Yes, the Reminders list item will update when a transaction is processed in QuickBooks Online. Let me share further details on how it works on the program.
When the recurring reminder templates run through, the data in the Reminder List section will not automatically refresh. It'll remain in that section, so you'll want to reload the page to see the updated list.
In case you need steps on how you can get a list of all your recurring entries and the accounts they're linked to in QBO, you can open this article: Review your recurring transactions in QuickBooks Online.
Should you have any other concerns or questions, just let me know and I'll be happy to help, Porterboys. Have a great day!