Do the headlight and windshield washers share the same pump? I can get my 09 to spray the headlights but not the windshield.

 

On the A6 they certainly do not share the same pump. There are 2 pumps - 1 for the headlights (which is higher up in the reservoir tank) and the windshield washer pump (which is the lowest pump if you have the reservoir out).

Quick search on ECS shows 2 pumps for your car as well:
https://www.ecstuning.com/Audi-B8_A4...Washer_System/