Do Not Disturb mode hides notifications in Android P DP2 (which Google unveiled and released at I/O 2018 on May 8) from the notification tray completely, so not only will you end up with no sound from the incoming messages, emails, and any other notifications, but you will end up with no visual representation of those notifications either. For anyone who wants to be able to completely disconnect from the world that keeps most people so connected without having to physically power their device down, Google's new implementation of Do Not Disturb looks to be the answer.
Worth noting is that these hidden notifications don't apply to every single notification that can come through to the phone. Do Not Disturb in the latest version of Android P will still show users notifications for missed calls and voicemails as well as system alerts, though it will also still keep them silent so you won't actually hear them come through when they do, essentially keeping it the same as it is for all notifications on Oreo. Users will notice that when notifications are being hidden from the notification shade the system will state that this is happening with a message that they're being hidden sitting just below the quick settings panel that rests at the top.
In addition to this the notification icons are hidden from the status bar too, so there is basically no way to tell if you have any notifications other than from the above-mentioned alert that says they're hidden from view. If users forget then notice this message, it's easy enough to tap the Do Not Disturb icon and disable it to once again allow notifications to come through, though users may want to expect quite a few of them if they leave the feature on for a while. Since this is the second developer preview of Android P there is always a chance that Google could change some things, so if you're not fond of the way Do Not Disturb mode works Google may always tweak things more.