Many developers have asked if they can use Pushpad for sending push notifications to their hybrid mobile apps. Basically they want to use the W3C Push API inside a WebView. That would make sense, because a WebView is a sort of browser embedded inside an application.
The Android WebView does not support the Push API yet. However the Android WebView will probably support the Push API in the future. You can check the current status of this feature in the Chromium Bug Tracker: Implement Push API and Notifications in WebView