The feature is working properly.
However, it's possible that something is getting caught in a spam filter somewhere. One of the things this function does is set the 'From:' header in the outgoing email, to match the email address of the group admin. It may be the case that your outgoing email provider sees this kind of "spoofing" and sends the email directly to spam (or perhaps your *incoming* email provider puts it in the spam folder - check there too). In my case, the email was sent properly, but Gmail intercepted it on the receiving end and sent it to spam.
As a test, you might try disabling this spoofed header. Open the file wp-content/plugins/buddypress-group-email-subscription/bp-activity-subscription.php and find the function ass_send_welcome_email(). At the end of that function, find the lines:
$headers = array(
"From: \"{$group_admin->display_name}\" <{$group_admin->user_email}>"
);
wp_mail( $user->user_email, $subject, $message, $headers );
Replace them with
wp_mail( $user->user_email, $subject, $message );
Then test the welcome email again. If it goes through this time, then the problem is indeed spam filters.