I put this code in the header.php within my active theme to test it out and it works perfectly on iPad and iPhone. I know the proper way to do this would be to make a child theme and put this code in a header.php file within the child theme, but for testing purposes this works.
It turns our there are apps for creating the icons at the appropriate resolutions. Search the app store. I did mine in photoshop.
In addition this is the code I found to customize the description that the “add to home screen” button provides by default. I think this solution will only work with iOS6 or above. Also you are limited to 12 characters. Replace “short name” with your 12 character name for the home screen