Trying to understand the working principle of a weird transformer driver / oscillator
It appears you're dealing with a variant of the Armstrong Oscillator. The transformer, together with the transistor and C1005 create a self-oscillating circuit and the voltage created across the primary by the oscillation is stepped up according the the turns ratio.

A sample of the circuit's output voltage is fed back to the primary via R1015, forming a voltage divider with R1001. Once the desired output voltage is reached, the OpAmp will "steal" base drive from the transistor, and it will then create a smaller signal - that's the control loop.

Running the circuit without the secondary will not give you the desired results, because you need everything around the control loop, but you might still be able to observe some effects without closing the loop (E.g. Will it start up at all?).

Since the basic oscillating circuit relies heavily on the inductance and capacitance values around the transformer and the transistor, you might need to be very careful with the parasitics, too. Also, what about the air gap in the core? It has a great influence on both iductance and possible core saturation.