Dont forget to AC couple the '1K' resistor to ground. The op-amp output is reference to half rail, not ground.
I have no idea whether this would produce good results. As I've mentioned before, I'm not a fan of applying gain inside the microphone.
Applying gain by using a low noise pre-amp will almost certainly get you better results. Even cheap audio inerfaces - like the Behringer UMC series - use quiet preamps these days.
Fitting extra gain resistors into the mic will almost certainly add noise -- and the higher value the resistor, the more the noise.
But this is a DIY mic forum, so experimenting is good... Give it a try and see how it goes!...