I think I am having the same issue. I am also with Godaddy and newly subscribed email addresses, with double opt-in enabled, are not receiving Confirmation and Welcome emails. I have confirmed this with an extra gmail address I have. I believe this was originally working (back around June), but has since stopped.
* I have enabled SMTP following the instructions for Godaddy
* I can send the test newsletters to the same email address, they are received in the Inbox