Well, first there is a difference between “notarization” and “sandboxing”. Notarization just requires you to have your app signed, is a completely automated process, and in no way restricts what your app does.
Sandboxing restricts what your app can do and you have to use entitlements to use certain features.
But no, notarization is not “required” and as an end user you can ctrl-click the first time you run an app to bypass it.