Technology still hasn't delivered a way of sending traction power through a non-permanent coupling, so the closest available method of operation to what you suggest would be to use the DMU to supply ETS to an otherwise-dead EMU... and that's not very far from how LNER already drag/push their electric-only Azumas around with their bi-mode ones (they just use a diesel generator on the 'pure' EMU to generate ETS).
It's a bit odd the first few times you hear the obvious traction motors followed by the burst of exhaust noise - but much less now that you can also get it from a diesel FLIRT