Ok - to add some facts to the speculation above:
I just made the front offside indicator open circuit on my van and then checked for error codes.
OBDII/EOBD: no predefined error codes generated. If some non-standard ones were generated, the tool I used didn't see them.
VCDS: no less than 8 error codes, including horn, power mirrors and a few others. The reports only identified that ~one~ of the front indicators was not passing current - the body control module did not seem to be able to identify which one. As soon as the bulb was reconnected, all 8 codes could be cleared in one go.
So, in the example I tested, VW's built-in diagnostics seem to act as a very crude tool for finding electrical faults.