Techone:
The spark is produce when the voltage is high enought to conduct ( die-electric of air ) between the two piece of metal of the plug. A bit like a capacitor when you apply a high voltage ( over the voltage capacity ) and the result is "POOF". The capacitor started conducting.
That's not quite how it works; you can find a correct explanation here. A modern mower ignition is still the same principle as a system using battery ignition.
It would be interesting to put a small load on the secondary to see how much power could be pulled off before the spark stops firing. Of course the proper course of action would be to equip your engine with a charging circuit -- assuming the flywheel has the necessary magnets -- or find one that has one.