Has a coil for powering cdi, not for spark. You pick spark in quotes beside ignition hinting that the ignition coil in the stator controls spark, it does not. Pick up coil sits outside the flywheel and sends spark signal to the cdi. Tend to worry if the first thing someone does on a banshee is check stator for no spark, probably verify your pick up coil is sending voltage to the cdi first, could be as simple as a loose pick up, gapped a mm too far to pick up proper signal, and you replace a $100 stator, problem isn't fixed, could have spend $15 and fixed it, sad faces all around. Now if your getting 3 or 4 volts out of pick up i would def check to see if coil was getting voltage, if it wasn't, i'd check cdi, and find that it had no power out, and realize i had a stator issue, it's ac cdi. Or it could be neither, your kill switch as eroded enough to deposit enough material for continuity across the switch and all tests don't matter...we can walk the slippery slope of well this couldl and that could happen.
If you are replacing your stator you had spark signal, no computer power to jump up the signal to the coil.
what happens when you have no spark on a dc cdi ignition system and you have trained your brain that stator controls spark? You chase your ass with a multi meter getting good readings on your charging system while your hunting ignition problems.