Probably not going to happen. Although GWR took over the service from BAA the Airport Lines are on BAA property and the conclusion seems to be they wouldn't give permission. It would also be an extension to the GWE route and DTG don't do extensions.
I'm pretty sure it'll never happen since GWR took control of the airport branches from Hayes & Harlington to Heathrow and 2nd of all. There's not that many stops, a route would contain many more. Heathrow Express isn't worth it.
GWR are only a subcontractor providing the trains and crews, the Service and Branch are still Heathrow owned