Our use case is a bit different, we only use Auth0 for machine-to-machine flows, so there is no user-facing login to direct a support email to. So my questions are:
Is the production check a hard pre-requisite for becoming a production instance, or just a strong recommendation?
Is there an option to turn this check feature off?
The production check is to help you detect common problems or configurations that are not recommended so it does not prevent anything in your tenant if some of the checks fail. To my knowledge there isn’t an option to disable specific checks although I confess I never tried to disable one.
Just as a personal opinion, I would configure the email provider using custom SMTP to an invalid domain. This way it meets the check and also guarantees that if you start using emails in the future you will be reminded to configure one as that one would not work.
