There are no quite lengthly connections, apart from in depots such as
Ruislip which has connections to the Central and Met. The longest one
outside of depots is probably Saint Mary's curve between Aldgate East
and Whitechapel connecting the East London Line to the District, used
for transferring A stock, which as you say is a short double track
tunnel section.

In general, only engineering train operators have a working knowledge
of more than one line.