> You can send notifications with PWAs with Web Push API + Service Worker, same as a regular page.

While the app is awake, sure.

I'd like notifications to work even if the OS backgrounded the app, and even without a network connection, like I'd expect a reminder to work.

> https://github.com/GoogleChrome/developer.chrome.com//blob/m...

Looks like this is what I need and it doesn't exist. So the short answer is "no". Thanks for the link!