Yes. Build your web application with responsive view features and add a json manifest file to let the android browser add it to the home screen as an app. The next time your users opens your app by clicking on your app icon in the home screen it will work like an app(full screen,no address bar etc.,) . You don't have to even put your app in web store.
But the API's supported are minimal compared to a full fledged native app.
The complete list of supported api's here . You might be surprised to see some api's like the battery api, offline storage so have a look.
Real world example:
visit aliexpress in your mobile browser and add to home screen.
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