Hi,
the registration page is the same of Joomla, so you can do this independently with Easy Profile.

I recommend you to use javascript on Register button with something like this:

jQuery(document).ready(function($){

    $('#member-registration input[type="submit"]').click(function(e){

        // here your code to show popup

        e.preventDefault(); // this block submit

    });

})

you can put on popup another button to submit form with javascript