If they don't choose a password - then a randomly generated one is emailed to them.
Tell them to use the "I forgot my password" feature and another one will be emailed to them, or you can edit their profile and set their password to something easy.
Emails should go out instantly.....
Threads just uses the mail settings in PHP (defined in your php.ini file).
If it's your server, you can make sure everything's set up correctly, if you're on a shared hosting, then you should ask your host why the emails are taking so long. But it gets sent by theads by the addpost.php script when the name is created.
