"mail() returns TRUE if the mail was successfully accepted for delivery, FALSE otherwise."
but this does not nesessarily mean the message was sent. it only means your mail server ACCEPTED the message, but what happens after that php does not know.
for example if you run a unix server and your sendmail location is /usr/sbin/sendmail
and in php.ini you set it to /i/dont/exists/sendmail
when you call mail it will return false because the message wasnt accepeted.
but if your server is unplugged from the internet and you use mail with the proper path in php.ini your mail server will accept the message but it wont be sent because you are offline. of course there are many other hangups that will cause mail to return true but have your message either be stuck in queue or never added to queue or sent at all.
so to be safe dont rely on that for determining if the message was sent or not.
if it is absolutely necessary, you may consider using sockets to send mail so you can connect directly to the mail server and see its responses.