When Soapbox Mailer processes your email campaign from Salesforce, it sends data to Amazon SES to tell it to send the message on your behalf. If Amazon SES confirms that it received the email send request from Salesforce and Soapbox Mailer, it will mark the Campaign Member record's Message ID field with an identification number. So, if you want to determine whether or not Amazon SES sent a message to a particular Campaign Member, you can just go to the Campaign Member record and see if there is a value in the Message ID field.
Happy emailing!