In the specific case of the 3R Tadpoles, the driving trailer was from an EMU, so probably originally had 3rd rail shoes though not the rest of the kit. Had they been formed using an ex EMU driving motor coach rather than trailer, the North Downs might have had bi-modes decades ago.
As an aside, those were three-car units with one-and-a-half cars of passenger space, since I never saw the DTS unlocked when I used
Would have been possible if the electrical gubbins was under the adjacent trailer.
It would have required power to be transmitted between cars but this was normal for a third rail emu, which had shoes on driving trailers.
I believe EP stock could multiple with DEMUs, although I never saw it happen. 33s and EMUs certainly could.
DEMU's couldn't multiple with EP stock as the wire functions in the 27-way way jumper were different.