@Medved
So you have a transformer with two identical windings (X-Y and Y-Z) connected in series so that their total measured inductance is effectively zero across X-Z. When you apply current across X-Z, the center node Y will gain voltage relative to the points X and Z (assuming X and Z are at equal voltage)? That sort of makes sense, but anything after that I am lost.
Yes, assuming the transformer has ideal coupling, so magnetic flux is exactly the same through both windings, so none could leak between them.
In reality you get some nonzero inductance, because the magnetic flux generated by one winding can squeeze without going through the other winding, this property of a transformer uses to be called "leakage inductance". How much it is depends on the exact arrangement. It could be few percents, or even 20..30% if there is really a space between both coils and/or even a magnetic shunt (a piece of iron core designed to provide that path).
With standard transformer you want that to be as low as possible, but with SRS some leakage inductance is beneficial, as it boosts the voltage across the lamp for ignition above the mains voltage.