You can check if an email has been successfully sent using the 'Dat_Email_History' table.
This table has columns on 'Date' and 'EmailAddress' which you can use to filter down the results.
The 'SuccessfullySent' column populates when an email has successfully made it to the end of our code. This means that as far as our systems are concerned the email has sent.
If the email was sent via RackSpace (Most of the emails generated on the website go through Rackspace) You can find out whether the email has successfully reached the recipient by checking the IIS Logs.
Only a small number of people have access to these logs so you will need to request it from someone with access such as Alan Kell or John Corker.