My answer is that it's possible, and pretty easy to check. Do you have the wiring print? I recently swapped my ignition due to proven bad contacting for START condition, and then we had someone else tear into their B. for some other things, but his ignition was the same as my L. The simple way to prove or disprove is to check. You just need to remove the cowling to get into the dash/switch. Disconnect the plug, Run the ohm meter across the HOT center lead and the ignition heater terminal. It'll be the wire that goes over to 1 side of the glow heater indicator (does on mine anyway). Do you know how to use an Ohm meter or continuity tester.
-OR
if you can get to the the heater element, See if you get 12V from the wire terminal to ground. Check each side while you turn the key.
the wiring diagram will show if you have a fuse in the system somplace as well.