Even now, there are hybrid engine "rafts" available for normal DMUs, either new build or replacement of the existing diesel package. These work like a hybrid car, in which the otherwise traditional drivechain incorporates a motor/generator and batteries to store power from braking to use during acceleration.
What if the electric motor on the hybrid raft was made bigger than strictly needed for the battery pack? Big enough that it was able to drive the unit by itself with the engine shut off? Not a wild idea, as even in motorcar-world there are plugin hybrids which can run exclusively electric for some trips, despite being more like traditional cars rather than electric cars with a "range extender" engine. The ones that spring to mind as I have seen them in the street are the Mitsubishi Outlander and the Toyota Prius.
Now imagine a pantrgraph/transformer car was cut into the hybrid DMU and a bus bar installed to take OLE power to the other cars of the unit, as per OP's suggestion. Maybe this transformer car could have powered bogies itself, to give more oomph under the wires?
Now what you have is hybrid train with the ability to use OLE electricity when available. I imagine this concept would suit predominantly unnelectrified routes with a small amount of electric running, since at heart it is a Diesel (mechanical) MU. Speculatively, all the mechanical stuff might make it more fragile than an EMU or DEMU. But on the flip side, being an evolution of traditional DMU and motor vehicle practice, it might be a lot cheaper to mass produce than proper DEMUs, and can be expected to be more easily retrofitted to existing DMUs.
