That is correct. The mail fuction returns ture if it executed correctly...There are a couple fo things to make sure of though as well.
1.)Ensure you sendto address is correct. If it's a variable there is the chance that it didn't get sent to where you think it did.
2.)If you have access to the server your working on check the maillog (whether it be exim, sendmail, qmail etc.) to see if it was sent or queued?
3.)Send the message or CC it to an address that you know should work this will enable you to determine if it's not being delivered at all or if it's just not being delivered to a particular address.
That's just some basic stuff that' I've ran into in the past. There is more then likely a way to check the SMTP server to see if the mail got sent via PHP if you don't have access to the maillog...I am not sure exactly how though. Sometimes your host will provide you with an admin panel.. i.e. Cpanel there you can check mail status and sometimes restart services etc.
Hope this helps.