electrical portion of ignition switches are known to go bad causing battery issues as you experiencing. Very common. Could be something else but most ly you're headed in correct direction. some quick questions to help diagnose...
Do you have to wiggle the key to get it out or to engage when turning on?
Does the ignition 'clunk' with key removal?
Do accessories stay on even after key removed from ignition?
Lots and lots of details, questions and DIYs in archives.
Search on any of the following terms:
- "how to love a woman like a contortionist in an 60's two-seater Alpha Romeo"
- "Help my dealer want $8,532 to replace a broken ignition switch"
- "clunk"
- "4A0 905 849 B" (the Audi replacement part number)
or go here:
Replace Ignition Switch for DIY details.
Good luck
