Push Pull Converter Transformer Saturation Rating
You need to do some learning here. Transformer saturation is almost 100% unrelated to load currents. If you apply a voltage to the primary, with the secondary unloaded, it will (largely) saturate no more or no less than under full load conditions.

I know this sounds unintuitive but any current in the primary that is due to secondary load current produces a magnetic field that is  totally cancelled by the magnetic field produced by secondary current.

If this were not the case then Faraday's law of induction would be violated.