On the blue will cause the same issue... shorting the blue to ground (just as shorting the white to ground) may well cause enough current to flow (briefly) for the winding to overheat, melt at the hottest point and open up.
If it measures open, it's dead... It would be an interesting exercise, however, to find out where the break in the wire occured -unwind, locate, clean, solder, insulate and re-wind it; returning it to life. I did this once, about 30 years ago with a bad magneto on a Yamaha. Not hard, just a LOT of turns of wire to unwind and rewind. And in the rewing process, if you're close to the original number of turns, it's good enough. If you're off by say 50 turns out of a thousand, it will only make a 5% difference in the voltage output - not noticeable IMO.
If one still wants to use the provided kill switch, I might suggest adding a resistor to one of the switch wires... I'll have to think a bit about the value. This would limit the shorting current to a value that won't kill the magneto. Since we know that the 6V leg is rated to about 1/2 Amp and I will assume that they use the same wire for both legs, I will assume that 1/2 Amp is safe for the HV winding also. Also assuming around 100V in the HV winding we can then solve for the resistor value that won't damage the winding. Using Ohms law - E = IR ---> R = E/I ---> R = 100 / (1/2) = 200 Ohm minimum value.
So we'll have to see if the kill switch will still kill the engine with a 200 Ohm or so resistor in series between the switch and the blue wire, with the other switch wire connected to ground. I'll try this soon and report back. One thing for sure, this should limit the kill switch's shorting current to a safe value. Hopefully, it will drop the magneto's voltage enough to stop spark generation.
The advantage of killing the engine this way is two-fold. It alllows you to continue using the provided kill switch (in my case, built into the throttle) AND it will significantly reduce EMI (electro-magnetic inteference) from the wire up at the bars which can cause havoc with a digital speedo.
Guess waiting for football has me bored enough that i decided to write a small novel here. Hope I didn't bore anybody to death.