It is not clear what you mean by "overall inductance". The equivalent circuit of a transformer referred to its primary has the magnetizing inductance across the lines and its leakage inductance in series with input. Hence, increase of leakage inductance causes increase of total inductance as seen from input. In fact several inverter designs use the controlled value of leakage inductance to create a low pass LC filter for the ac output voltage without using a separate physical inductor.
Negligible leakage flux, due to low reluctance path offered by CRGO core and low magnetizing current, would not make any considerable change in generated voltage or the power out put of transformers, if utilized......