Previously, each Branded Website required it's own unique email address, and technically it still does, however that email address does not need to be a "working" email address or alias.
Reminder: By default, the Site Owners email address is used for the "Reply-To" address when a customer responds to an email notification.
We've added the ability to change the "Reply-To" address to anything you'd like. We recommend using a common email address among all of your Branded Websites such as email@example.com
From the Admin Menu, navigate to Site Settings, Options, Shop Email Notifications: