Based on what has been posted so far, the only downside may be that your RNS-E will completely power off later than necessary. If that wire is the only one missing and everythign else is correct, you may be fine just leaving it as it is. Or get a couple repair wires the next time you are at the Audi dealer and fix it yourselves without getting a new adapter.
My previous adaptor did not have that wire, and everything worked just fine. There were no delays in powering down (in a 2002 C5 A6). My current harness has this wire, and there is no noticeable difference. I think NSX JR mentioned tome a while back that the only difference with that wire missing was if the headunit is taken out, it is not tied into the car's alarm. Of course, if someone broke into the car already...shouldn't the alarm be going off already (assuming the car was locked properly).