Sorry, your method will not give useful information on the capacitances that determine the PU's resonance(s). The equivalent circuit of your arrangement consists of the series wiring of two coupled windings of a transformer with distributed and reflected capacitances and a rather small interwinding capacitance (<50pF or so) in between. (Please see thread titled "Switchable additional winds"). The result will be more or less the interwinding capacitance. But this does not relate to any PU resonance.
You can measure PU capacitance with an LCR meter that allows measuring at 100KHz. With typical high impedance PUs the accuracy is very good. The absolute measuring error (always negative) caused by the presence of inductance is below 3pF for a PU inductance of 1H and decreases proportionally with higher inductances.
Generally the importance of PU capacitance on the frequency response seems overrated. Its impact on the loaded resonant frequency is much smaller than inductance. A difference of 100pF corresponds to a 3 foot change in length of a typical guitar cable. Thus cables of different lengths can be used to evaluate audible effects of different PU capacitances.