Hi @mikkelm , welcome to the Auth0 Community!
You’ll be able to configure the custom domain whilst still continuing to use the Auth0 domain, this is stated in our docs here, as well as in a commonly asked questions post about custom domains here , (Question 5.)
As you can see on the docs page, once the change has been made in your applications, users will need to log in again as the existing sessions will be invalid.
Hope this helps, thanks