... And of course Underground stock is fourth rail, so some modification, either of the stock or the track, would be required.
Converting 'fourth rail return' to current return via running wheels is definitely not trivial. Just because you cannot really see anything obvious on a typical third rail
EMU▸ doesn't mean it isn't quite different. Basically you have to distribute the return current to many wheels (to reduce the current per wheel), and you cannot allow current to flow through the wheel bearings, so if you look closely you'll see a brush box on the outboard end of many of the axles which transfers the current to the wheels while bypassing the bearings.
(The third rail shoe has a much larger surface area than the wheel/rail contact area, so as to reduce the resistance to a similar value you need significantly more contact points.)
In extremis it could require new bogies - and
IIRC▸ one of the key features of the conversion is that the existing bogies are retained.
On a shared LU/
NR» route the LU stock still uses the fourth rail normally, but it that rail is electrically tied to the running rails and the LU stock sees the 650 V
DC▸ on the positive shoe gear, and 0 V DC on the fourth rail shoe.
Paul