[hawaiian]

You can turn it off under Screen Time -> Content and Privacy Restrictions -> Allowed Apps.

[Nextgrid]

There's no guarantee that restricting access to the UI of the Mail app would prevent it from refreshing accounts in the background.

[hawaiian]

I was under the impression that it disables it on a deeper level since disabling Camera, for instance, disallows apps (like Snapchat) from accessing the camera even if you'd previously given Snapchat camera permissions.