Solution
The C-series modules do indeed offer different conversion times based on the ADC mode of operation. This also impacts the noise in the signal as high-speed mode does not filter for noise, while high-resolution mode effectively eliminates 50/60 Hz line noise.
The primary difference in their operation is in the period of time the ADC spends on processing the signal.
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High-Speed mode: The ADC oversamples and digitally filters the input signal over a small period of time.
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High-Resolution mode: The ADC oversamples and digitally filters the input signal over a much longer period of time. This is usually long enough to filter out both 50/60 Hz noise
You can certainly acquire data at the maximum rate in High-Speed mode and then implement your own filtering in the host to increase resolution. However, the results won't be exactly the same as what the module does internally for High-Resolution mode. In particular, these results will be different because they won't be continuously oversampling and averaging over the entire time since every new sample in High-Speed mode will reset the ADC filtering process and start over.