Yes, that's a pretty accurate description.
The diagonal lines, apart from Central Line to West Ruislip, Bakerloo south of
Baker street and Picadilly after curving (as you describe) n. from Picadilly
Circus to Finsbury Park, are short links like the South Acton spur, the
Kensington Olympia, and New Cross. And yes, joint sections are shown as double
lines.