Yes, it matters a lot.
For a signal with a frequency of 100 kHz you need an ADC with at least 200 ksps. The ADS1220 is only 2 ksps.
I haven't worked with such a weak signal but you can see the circuits with an operational amplifier as an ideal rectifier diode. Then, depending on what Arduino you use (you didn't say), its built-in ADC may be appropriate.