Even when SMTP is enabled for bulk mailings welcome, confirmation, and notification messages all use PHP internal mail(). It's possible that this function is not supported on your server. To test, toggle the mail sending process from SMTP to PHP mail() and send a test message to a test list that normally works. If you do not receive the messages with PHP mail(), but do with SMTP, then you'll need to talk to your host about availability of the mail() function.
Regards