Hi Nick, it's not possible to set up any kind of authentication to the Node-RED dashboard, i.e. where a user would have to enter a password. (Others may correct me if I'm wrong, but my understanding is that Node-RED is a single user system, and the dashboard is conceptually a layer on top of this single user system. There is no support for multiple users therefore authentication of multiple users.)
However, if you don't need security per se, then what you want to do is definitely possible. Let's say you just want a user to view a dashboard page and register their email address, and for notifications for a given thing to be sent to that email address, then yes this would be possible. You'd need to make your own user registration system.
See @nygma2004's youtube video, the opening screenshot shows a kind of user registration page (although the input to this actually happens externally to Node-RED rather than within the dashboard - but it's definitely possible to do within the dashboard), and he explains and makes available various stuff for you to play with. This particular vid doesn't do exactly what you need (i.e. ability to enter email address) but it does show a user registration system where you can change other aspects of the user's registration, update fields / delete / etc.
Hope that helps