Noise will vary very little as device operation approaches dropout. However, PSRR will be affected is the load current is such that the device is actually operating in drop-out mode.
Cff (across R1) is not required, nor recommended. Cff is typically used to add phase margin to an output power stage feedback loop with capacitive loading, In this case, R1 and R2 are used to set the DC reference voltage which is isolated from the output power stage by the low pass filter.