First of all, thank you for this wonderful plugin I want to ask a question about social media login.
I tried to use WP Social Login profile but the users mail isn’t synchronised with the existing account. Also I can not create the new account with Facebook, Twitter etc. I’m sure I configured the API’s perfect.
Okay what I understand from your questionis: You want user to register from Social Login plugin and send them email using PR email notification system. If this is case then I am afraid you can not do. PR doesn’t work like this.
You may be able to use Oneall Social login with Pieregister. On their site they tell you the hooks you can place in your php files to add the option to things like your comment form. You can add it to a page by shortcode or by its php code. It is free but if you some extensive css changes to it then you will have to buy basic plan. They also mention on the site how the wordpress database isn’t prepared to add such fields from a social network profile and they though give you an idea where to start with a code snippet example you have to place in function.php
I like this but havent been able to implement this plugin due to lack of buddypress support so I had to use User Profiles Made Easy. No bbpress this would be my first choice. They are keeping this free so what can you expect? But with bbpress and buddypress support they could take UPME down very easily. Hint Hint.