Still didn't answer his question - if Quickbooks has the capability to email an invoice, it should have the capability to email a notification to a specified email (the QBO user) that an email to a particular recipient (customer) failed.

This has happened to me on numerous occasions.  I think an invoice is past due and only discover when going into the invoice that it was never received by the recipient for one reason or another, and I lose days or weeks on A/P processing because of the problem.