Sorry for late reply. I was away on travel for work. So, what you would like is to have a way to display a form asking users to provide their e-mail, then show them the link. This functionality is not provided by the plugin by default, but there is probably a way to add it. One way I can think of would be to use the existing pop-up functionality where the plugin can display a pop-up window with custom content.
In that pop-up, the link could be hidden until the user enters his e-mail.
What should be done with the e-mail after? Should it be itself e-mailed to the site admin? Or would it need to be stored somewhere?
While the majority of this could be done with the current plugin, doing it would require a fair amount of knowledge of Javascript and jQuery, along with some modifications to the plugin. Are you knowledgeable in the first two areas? If not, I would need to implement all of the code needed and this would require some financial support.
What is your timeline for this project? I am not available to work on this until July.