you will have more leakage inductance, anything in the core window which is not an active winding represents leakage inductance, that is why they try to fill the window up to the brim with wire. not so for power transformers because all they care about is 50/60 Hz.
so insulation between layers and pri/sec sections represents leakage inductance, as there is less wire to catch the flux set up in the core, but insulation also reduces capacitance, so it is a balancing act between leakage inductance and capacitance, so you can tune a transformer's response by altering insulation thickness and type,
it may turn out that the un-sused winding will reduce capacitance and actually improve response, but the transformer will drop level faster when loaded on the secondary side with a resistor etc.