Sorry for the delay. Unfortunately, because this question was posted as specific to this plugin, no one else responded even though this behaviour is not caused by this plugin, and you’ve also eliminated the Custom Login plugin with your own testing.
e-mail problems like this are tough to figure out because there are so many ways that an e-mail can get lost. In your original e-mail to me, you also asked about the Return e-mail address used in some of the e-mails that do get through.
Starting with the easy answer first: the E-Mail Address field on the General Settings page of WordPress Admin /wp-admin/options-general.php determines the sending address for your site’s outgoing e-mail, including New User notifications.
Your previous e-mail to me indicates that some User e-mails are getting through from WordPress, so this is not an “e-mail functionality is turned off” type problem. My best guess is that this is some sort of Spam Filtering problem. Which means, the first place to start would be with your Web Hosting Support folks. Ask them where to find the Mail Logs for the period of time when the missing e-mails should have been sent.
The Mail Logs will certainly tell you if the e-mail actually got sent by WordPress, which it very likely did. It might also tell you if the User’s Mail Server was rejecting all e-mail from your Mail Server (in my own case a while back, it was a Reputation problem because of someone else sending Spam). Of course, if the User’s workstation software is putting it in a Spam folder, the Mail Log will merely verify that the message was sent.
As I say, this has nothing to do with my plugin, but you may want to verify that by deactivating my plugin and creating a user ID using the Send Password? checkbox in Add New User http://localhost/wp/wp-admin/user-new.php
