The line will be an orphan whether or not it transfers to Chiltern, as no other Great Western services will serve West Ealing after May 19th. It will be Central Line at one end and TfL Rail at the other.
The line has a very close counterpart in East London (shuttle service connected to the Underground at one end and Crossrail/TfL Rail, Elizabeth Line at the other, but isolated from the rest of the Overground, and entirely within the GLA area. That line has been Overgroundised, and at first glance, the Greenford branch does indeed look like another candidate for Overgroundisation. However, unlike the Emerson Line, the Greenford branch is not electrified. The Overground is busy eliminating its only existing diesel line, and would not want to have to retain (or hire in) an odd diesel unit specially for the shuttle.