No it doesn't.

IN LON-on the TfL system you CAN use it on the LON OVERGround trains-that used to be long time ago normal BR-lines/suburban but have been taken over by what once was ´London Transport´ with then world-wide fame. As the name indicates, they run for 99% OVER the ground and not under. For the normal tourist they will be of hardly any interest, for locals it will depend where you live.

However, its gate-staff, certainly at minor stops, is often not familiair with it and may/may not object.

Yes, the areas of London Overground serves are usually quite a way out from the centre. There are areas of touristic interest in these parts of London (particularly for cuisine, food markets or nightlife), but they aren’t the big ticket sightseeing draws.

You may find Thameslink and Elizabeth Line trains a bit more useful to you. They are also covered by Interrail passes, and they cross central London N-S and E-W (with the crossover point where the Eurostar comes in at St.Pancras)

The interchange between Thameslink and Elizabeth line is Farringdon. The Elizabeth line is not fully operational and is usually closed at weekends 

So it is, apologies!

Many thanks to all the replies. For a first time interrailer they were most useful.