I think it is possible. Look at the documentation :
h ttps://developer.apple.com/library/content/documentation/NetworkingInternet/Conceptual/RemoteNotificationsPG/SchedulingandHandlingLocalNotifications.html
If your app is not running, or if it is in the background, the system displays local notifications directly to the user. The system can alert the user with an alert panel or banner, with a sound, or by badging your app’s icon. If your app provides a notification content app extension, the system can even use your custom interface to alert the user. If your app is in the foreground when a notification arrives, the system gives your app the opportunity to handle the notification internally.
NOTE
Local notifications are supported only in iOS, watchOS, and tvOS. In macOS, apps do not require local notifications to badge their icon, play sounds, or display alerts while running in the background. Those capabilities are already supported by the AppKit framework.
Did you watch WWDC ? There are 2 sessions on notification, notably this :
h ttps://developer.apple.com/videos/play/wwdc2017/708/
Best Practices and What’s New in User Notifications
Session 708 iOS, watchOS
Local and push notifications enable your app to keep users informed with timely and relevant content, by displaying messages and accepting users' actions, or playing distinctive sounds, or updating the badge on your app icon. Service extensions enable your app to decrypt and augment push...
I think the second one is less relevant
Rich Notifications
Session 817 iOS, macOS, watchOS
Discover the keys to creating informative, useful and beautiful rich notifications in iOS. Get practical and detailed guidance about how to design short looks, long looks, and quick actions that will make your app's notifications something people look forward to receiving.