Record/copies of PHP mail() previously sent from our website?

Should there be a record of all php sent mail (via our hosts mail() function) anywhere?

Our web developer made an oversight and all enquiries sent via the our host's (godaddy.com) mailer relay for the last 2 months were rejected by our local mail server. Naturally, our server doesn't keep any rejected emails.

I have spoken to godaddy.com and they claim there is no record, however I'm not particularly confident with the answer.

Is there anything I can do? The enquiry form is now fixed (used Mandrill), so that's not an issue.