Yes, web apps can send push notifications to desktop and mobile devices of users. 

To send web notifications, there is two way you can do it.

First, you can set up your own notification platform. However, setting up your push notification platform requires time contribution and a lot of resources. 

Second, you can integrate with the existing push platforms. For example, you can use Truepush for free with no limits on the number of notification campaigns or number of subscribers. 

You can also set up your PWA push notification and AMP notification using Truepush.