Using ADS1252 In DIfferential mode
It looks to me that the ADC is running in diff mode. The input amps you see provide a converting stage to transform a uni-polar single-ended input (~0-5VDC) to a differential input to the ADC. A strategy to boost resolution. This circuit is not designed to accept a differential signal as an input. It may be possible to hack the design if needed (you would need to cut some traces). Do some more googling. 

Re, the circuit as is: No, it is a single-ended to diff converter. It allows one to connect a native single-ended signal to a differential converter. It will help with the resolution of the conversion of the single-ended signal, and that's about it (there is some minor filtering going on, but nothing terribly aggressive). 
You'll be fine to not implement this circuit, if you already have a true unipolar differential signal (be certain that you do!). A true unipolar differential signal will have two signal wires. The signal on one will mirror the other. As one signal goes from 0 to 5, the other goes from 5 to 0.  Only positive voltages, and be wise to stay away from either rail, 0 or 5V (Consult the datasheet of the ADC). 
In addition, there should be a ground reference from your signal circuitry to the ADC ground.