Yes, you can intercept anything, using middleware, for example.
But, for some reason I the ability to disable the "new user registration" UI was already implemented in Sphinx, but it's not. So I think this is a different feature request.
I created that one here:
Thus, one thing is the ability to disable user self-registration (the above feature request).
Another thing is the ability to create a new user from code and ask for invitation (this feature request).
Although if you require e-mail confirmation, even if you create a new user from code, user will have to confirm his e-mail to create the account, thus I'm not sure if this feature request here is still meaningful?
Disabling in the UI only hides the link. Anyone that can hit F12 in their browser to view the source can see the link that is hidden can copy it or follow it to continue the process and register. Need ability to remove it completely for some of us. Hiding it is a temp solution.