Check your mail server's mail log. On Unix-ish systems, it's generally /var/log/maillog. On Windows, who knows, but there should be a log somewhere. If mail is returning TRUE, then whatever mail server it's connecting to has accepted the mail for eventual delivery. After that, mail() is no longer involved in any way and it's up to the SMTP servers to do the actual delivery.
In real world terms, mail() is you walking a letter down the block and dropping it into a mail box. Everything after that is utterly outside of PHP's scope and control.