For iOS, can't you just wrap your web application in a thin native app layer that provides the push functionality?
4.2 Minimum Functionality
Your app should include features, content, and UI that elevate it beyond a repackaged website. If your app is not particularly useful, unique, or “app-like,” it doesn’t belong on the App Store.
The important part is that they go through the app store, so that apple has complete control of what goes through.