What happens to the gain of a switched capacitor circuit when a resistor is placed in series with the input voltage driving source?
Your question touches a typical problem of all S/C circuits because the real on-resistance of the switches must be considered during the design of S/C blocks. Of course, such an on-resistance is nothing else than a series resistance together with an ideal switch. 

Hence, the answer to this question is as follows: As long as the resulting time constant RC is sufficiently small if compared with the time available for charging the capacitor (50% takt period) the function of the S/C block will be (nearly) not altered. If the resistor is too large the capacitor will not get fully charged and transfer errors will occur. Typically, this problem always sets the upper limit for the takt rate.