No, it wont. If you've got black oil 500 miles after an oil change then you are running on the old filter. In my experience, it gets "black" after about 4-6 k miles. This goes especially true if the car is relatively new and the oil changes done in a timely manner.
Originally Posted by quality_sound
After about 500 miles that "new" oil will look just like oil that's been in there for 5 or 6 thousand miles. This would be a good check to do at the dealership though, assuming you still distrust them enough to feel the need to check.