I researched the topic a little bit and as far as I understand now it's not possible to add a web-app to the home screen programmatically, but may be there could be a work around.
As far as I'm aware it cannot be done programmatically (which makes sense since there would be obvious security/usability issues if every page could add its own home screen icon). The link you provided refers to the menu option that the user can choose.
And if it could be done only on user input?
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Ashley is saying it has nothing to do with C2. It's the Feature of the Browser + OS. You will have to check how it's done by checking on Chrome for Android information.
Yeah, I understand. Just wanted to raise the topic, because I think it's kind of important for HTML5 developers.
There is no way to do this automatically from the web page, at all. So it is not something we can add.