Simplifying capacitor input network
This question has a very simple answer: Yes. 

Because in practice the capacitors are not ideal, things may change a bit. 

Because in practice the opamp won't be ideal, the shown circuit will probably not work. The input pin of the opamp will consume a very small current. Often nano-amps (1000th of a micro-amp!) or even pico-amps!

With only capacitors connected to the input pins, that will fully charge or discharge the capacitor and might end up with a circuit that is locked against a power supply rails....