Answers, I think:
1. You know it gets more sensitive, so does the designer. Therefore the reactions of the autopilot are "slugged" as it gets closer. But don't forget, the drift will have been calculated a long while back, so you wouldn't expect large heading alterations once this has been determined by the system. As for the appropriate tracking tolerances, these are published all over the place (JAR/OPS etc...) and they all depend what sort of airspace you are in. Generally though, you wouldn't use a VOR "raw data" unless forced to do so. The FMS is a damn site easier!
2. It should do, but...