Will Intuit charge me fees for invoices sent to and paid by Network Connections?

It's great to have you here in the Community, edward.

I'm here to share some details about the transaction fees.

Once you cancel your QuickBooks Payments account, you'll no longer get charged since this add-on feature only asks for fees every time you process a transaction. Since you already used a third-party application, rest assured that you won't receive any fees when you send your invoices and get paid. 

You can always get back to us if you need further assistance. The Community is here to help. Have a good day.