No that doesn't make sense. I probably can't discuss this properly without seeing a wiring diagram but let me tell you what I think should happen.
With the crash module disconnected the MIL (malfunction indicator light - ON DASH) should be lit. With the sensor connected and the car running the light should go out if you are getting a proper code 1 (one flash when testing).
With the crash sensor unplugged the led (used for impulse testing) should be unlit UNLESS you are grounding the socket #6 at the moment.
With the sensor plugged in the led should not be lit when just plugged into the #6 socket. It should light only when the ground activation is happening or when the sensor is flashing out its answer.
Actually I think I understand your sentence: "light does stay on with the crash semsor unplugged unless I ground pin#6" now. You are talking about the inside MIL.
Read my above statements and see if they apply. If you are getting a flashing code one I would verify the above conditions and look at the MIL wiring. I suppose the sensor could still have a problem without the code being flashed but it would be very unusual.
Bosch Master, ASE Master, L1
33 years MB technician