RF over sampling to increase SNR
Assuming the PIC has an analog input capable of operating at 32MHz or significantly higher than 9kHz (Nyquist Frequency), then yes it is possible to use averaging to increase the SNR.

It is important to consider the issues with respect to your SNR. For example, if the SNR is low due to transmission distance (attenuation), then averaging may not be very effective, whereas if transient spikes or emi are the source of your issues the averaging could be very helpful.  In both cases, you may decide you need a hardware solution such as a pre-amlifier or a bandpass filter respectively.

I suggest you use an oscilloscope to look at the eye diagram, this will help reveal the specific problem with your received signal.



Silabs have a useful note on oversampling and averaging here.