Do remote push notifications require to add UIBackgroundModes in Info.plist?

Yes, you should enable Background Modes/Remote notifications to be able to use remote notifications for background updates.

The easiest way to do this is via the project settings. Navigate to Targets -> Your App -> Capabilities -> Background Modes and check Remote notifications. This will automatically enable the required settings.

You can also edit needed info.plist (Open As -> Source Code) and paste :

<dict>
<key>UIBackgroundModes</key>
    <array>
        <string>remote-notification</string>
    </array>

In fact, you do not need to add UIBackgroundModes to .plist simply to use remote notifications.

I know I'm splitting hairs a bit (the other answer is mostly great, and perhaps something is new as of iOS 11), but the question refers to push notifications necessitating background updates, and they do not.

The distinction here, is that there are two different methods that accept notifications on the AppDelegate;

This one does not require you to use UIBackgroundModes:

optional func userNotificationCenter(_ center: UNUserNotificationCenter, 
                         willPresent notification: UNNotification, 
               withCompletionHandler completionHandler: @escaping (UNNotificationPresentationOptions) -> Void)

The above replaces the deprecated as of iOS 11:

optional func application(_ application: UIApplication, 
didReceiveRemoteNotification userInfo: [AnyHashable : Any])

And this one does require background modes capability:

optional func application(_ application: UIApplication, 
didReceiveRemoteNotification userInfo: [AnyHashable : Any], 
   fetchCompletionHandler completionHandler: @escaping (UIBackgroundFetchResult) -> Void)

The key thing here, is the former one (and the deprecated one it replaced) only runs when the app is in the foreground. The latter will run if the app is in the foreground OR background. See the spec for this specific nugget:

Use this method to process incoming remote notifications for your app. Unlike the application(_:didReceiveRemoteNotification:) method, which is called only when your app is running in the foreground, the system calls this method when your app is running in the foreground or background.

Hence, if you need push notifications, then decide if you need to run in the background - only if you need both should you implement the method suggested by the warning.

Select your .xcodeproj file from Project navigator then go to Signing & Capabilies and then from library (command + shift + l or Click (+ Capability)) search for Background Modes after that, drag and drop it to Signing & Capabilities then check Remote notifications and Background processing. Also (important) add Push notifications by clicking + Capability