Offset and gain will not be specified with the same level of accuracy (or at all).
If you only do AC measurement, offset is irrelevant. Note the ADC you mention in the datasheet has a digital DC blocking filter (high pass) which can be bypassed via I2C configuration to make the ADC work with DC too. I don't know if the Cosmos allows you to do that, or if the analog frontend passes DC or not.
Gain will probably be specified under "full scale digital corresponds to ... dBV on input" or something like that ; ESS chips have some variation of gain between chips or between channels, which is usually compensated for by the internal volume control. Basically, you have no out of the box accuracy on gain, so you have to calibrate it. That's not really a problem.
Same thing for frequency response, phase, etc, it depends on the frontend circuit in your box.
Boxed ADCs usually have volume pots, which means once the calibration is done, the pot should not be used anymore.
On a "real" measurement instrument you would find rotary switches (or relays, etc) having discontinuous accurate settings, ie you can increase gain by an accurate 10x. With a pot, you can't (you can use fixed attenuators).
You won't have any specs on gain and offset stability vs time, temperature, etc.
This means a signal source of known accurate amplitude, or an accurate AC True RMS voltmeter, are needed for calibration if you want to get "real volts" out of your soundcard data.
Besides that, they work absolutely fine as low noise, low distortion, and especially low cost ADCs. No problem at all.
You can use a soundcard for a wide range of measurements by building your own analog frontends and software. It makes a great low frequency network analyzer, but that's only the beginning.
The main feature in a soundcard is synchronization between DAC and ADC. If you use the DAC to make a stimulus signal, run it through a DUT, then acquire it with the ADC, when ADC and DAC are synchronized you can measure phase lag from the DUT, or average a low amplitude signal over many periods to reduce noise.
Separate DAC and ADC not using the same clock are less useful because the recorded data won't be synchronized with playback data.