Something can still work, even if not fully or correctly yet still flag a fault, if the resistance is too high or too low. It could be other changes rather than just the N205 that affect the idle, as during the same cold start procedure, there is also a period of dual fuel injection where the injector fires twice.... again aimed at warming up the cat which could be affecting this.
VCDS will tell you for sure whether the cam adjuster is doing anything. To be honest I didn't see what fault codes you'd picked up previously - too many pages to go through! Let us know what happens when you get an N205 on there. Might be worth going to a few scrapyards to find one as I'm pretty sure its the same part on most if not all 2.0 TFSI lump
Typically I always see this thread when I'm in work and can never view any media