No!
Pinwheel uses usernames and passwords for our devices so that kids won't need emails to use Pinwheel.
However, many third party apps available for the Pinwheel phone are not as forward thinking, and you may need an email for your child in order to use those other services. We recommend the privacy-focused service ProtonMail if you want to set up an email for your child for these other services, they are based in Switzerland and thus have strict privacy policies.
You can add ProtonMail's client app right to your own iPhone or Android phone and keep it separate from your main email that way. It is also available in the Pinwheel app boutique