Authentication Options

I am interested in this registration form for an upcoming event we are planning. I would need to be able to customize the form with options and have the user be able to input their information.
But, the main thing I am looking for is this. This event is a ‘by invitation only’ event. So i would like to have the user click on the link to the registration portion and receive an authentication popup where they are required to input their email and name. If the info the user inputs matches the list we have, they are taken to the registration page. if not, they are asked to contact the adminstrator.
Is this something this particular plugin can do?

Thanks,

https://www.ads-software.com/plugins/custom-frontend-login-registration-form/