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For a PIC 16FXXX working at 20MHz clock, i calculate a maximum of around 31 k samples /s for 10 bit conversion and not considering the processing time.
A/D conversion needs sampling period (10 us which may be greater depending on the temperature and output resistance of the signal source) + conversion period (12 x Tad = 20 us) + 2 x Tad.
At 20MHz, Tad can be 1.6 us (Fosc / 32), so no way to get less than 16 us only for conversion.
What do you want to sample? only one pulse or the RMS value of a train of pulses? I will smooth the signal with a cap and then sample the RMS to sample the amplitude of one pulse is not possible because you don't know what the state of the pulse is when the sampling start and there is no way to determine this
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