Users can alter their own preferences for recieving notfications about assignments.
By default users can turn these off, you can see what I mean by looking at your own notification settings here on Moodle.Org:
1) Click the "bell" notification icon to the left of your profile image in the top right hand corner
2) Click the "cog" / "gear" icon to go into notification settings
From there you will see on the top row you have the ability to disable email notifications for assignments.
We actually lock those settings to "on" to prevent students disabling assignment notifications so in our case what I am suggesting would not work, but I think by default Moodle allows users to control those settings, so there is a good chance those teachers will be able to disable the notifications if they want to.