Notifications Drawer

We are working on a desktop app with lots of events/alerts/notifications. Because of that, we created a 'notification drawer', similar to the this one:

My question is: do you expect the snackbars and banners (that generate the notifications inside the drawer) to keep appearing (outside of it) when you have the drawer open? or would you just let them know (somewhere in the drawer) that they have new notifications and they need to update the panel?