Thank you for reaching out to us here in the Community, @tburch. Connecting existing customers through QuickBooks Business Network has yet to be made available. Creating a new customer is the current option to connect your customers to QuickBooks Business Network. I recommend you add your vote for this one by sending a feature request in the Feedback section within QuickBooks.
For your future reference, I would like to share this article with you: Create and send customer statements in QuickBooks Online.
Please don't hesitate to reach out if you have any questions about QuickBooks Business Network. I'm always here to assist you. Have a fantastic day!