I am sorry. this is incorrect

The pickup itself vibrating has no effect whatsoever on the sound.
To prove it get a bass and record it. Then take the pickup out and have something not connected to the bass hold it on the other side of the strings, the same distance from the strings.
Make sure that you play over the same part of the string in the same location. The bass will sound the same through the pickup.
Pickups pick up magnetic field changes from metal strings passing through it's magnetic field... pickups do not sense ANYTHING about physical vibrations directly.
The Strings however are the ones that "sense" the physical vibration directly, and react directly to different woods, tone blocks, bridges etc.