Is there current flowing through this capacitor?
Consider this picture: -



The voltage at the non-inverting input is \$A\times\dfrac{XC_2}{R_2+XC_2}\$ and, given that the op-amp is configured as a unity gain buffer (gain = 1) the output voltage is the same.

This means that the voltage across C1 cannot be zero and hence current will flow through C1 if that voltage has an AC signal content produced by Vs. If the voltage produced by Vs is purely DC then no current will flow once the circuit has stabilized.