I hate to disagree with Noob - he is always the man - but I work on a daily basis with airbag electronics. Not VW, other OEMs. Most airbag controllers are connected to dozens of external sensors, airbags, etc. These connections are continuously checked by the controller. If a fault is found, the airbag lamp goes on. If the fault does not recur, the lamp goes off after 10-20 ignition cycles.
More serious faults get "latched." Then the lamp stays on until you go in and clear the fault. I haven't had the occasion to do that with my VCDS so I don't know how that works on VWs.
Edit: Also, in most cases the bags will still work with the lamp on. You just can't be sure everything will operate correctly. It depends on the fault that turned the lamp on.