Unfortunately there is no way that one can track email sent through the system (that is without keeping the log files turned on to Debug mode and growing very large rapidly). QC is not a mail handler, and just hands the request off to your SMTP mail handler. In the event that the mail is not delivered then it will show up within the Site Admin as and error and will be held and retried to send at intervals. In this case the error log would contain the mail sent tries for that errant mail attempt (and all others pertaining to that errant mail).
If you have a managed SMTP portal within your IT configuration you could contact you IT Mail administrator and possibly get that information.
I hope this helps,