Yes, GoNative is designed to work with any mobile-friendly website already hosted on the internet.
If your app works on Mobile Safari on iPhone, it will work the same way in your iOS app. If your app works on Mobile Chrome on Android, it will work the same way in your Android app.
You may test it out by entering a website URL at https://gonative.io/new. Please see some examples of recently published apps at https://gonative.io/examples.