When attempting to place an RC filter directly in front of a switched-capacitor ADC (the typical kind), it may be important to ensure either that the capacitance is very big, or that the RC time constant associated with it is very short. Since the whole purpose of an RC anti-aliasing filter is usually to have a time constant which is much longer than the sampling period of the ADC, using RC filtering on the input of an ADC can often cause problems.
Further, even if the behavior of an amplifier is only specified up to a particular frequency, that does not imply that the amplifier will harmlessly filter out any input content above that frequency. It is very common for input frequency content which is outside the range an amplifier's useful range to cause unwanted distortion effects within the amplifier's range. A guitar amplifier, for example, wouldn't be expected to amplify cell phone radio signals (which are over a thousand times higher than any audio frequencies the amplifiers should handle), but cell phone signals will cause very audible interference nonetheless.
Because of these factors, I would suggest that there be sufficient low-pass filtering before the early amplifier stages to prevent unwanted high-frequency content from causing distortion. Some RC filtering on the back-end may be okay if R is small and C is large, but the rear-end filtering should only be designed to minimize noise that gets introduced between the amp and the ADC; such noise is going to be dominated by frequencies that are orders of magnitude above the highest frequency of interest, so the cutoff frequency of that filter can be far above Nyquist.