Chrome on Android now supports a meta-tag mobile-web-app-capable:
Since Chrome M31, you can set up your web app to have an application
shortcut icon added to a device’s homescreen, and have the app launch
in full-screen “app mode” using Chrome for Android’s “Add to
homescreen” menu item.
For details about the mobile-web-app-capable meta-tag, scroll down to “Supporting homescreen-installed apps prior to M39”:
Since M31, Chrome will look for the following meta tag in the
element of the web-page (if there’s a manifest with display specified,
this is ignored):
<meta name="mobile-web-app-capable" content="yes">The name attribute
MUST be “mobile-web-app-capable” and the content attribute must be
“yes” (case in-sensitive). If there is any other value in the content
attribute the web app will be added as a regular bookmark.
While I don’t have any devices running Chrome M31 that I could test with, I interpret this to mean that full-screen web apps, with an icon on the device’s homescreen, are supported as far back as Chrome M31, provided you use that mobile-web-app-capable meta tag.