I have no idea how balanced audio works when connected with only the positive voltage of an unbalanced audio.
Like does it clip in this case at 2V or 4V?
Probably not (Note -I don't know the input circuit of the flex, the following is based on my expectation of how it will work)
The balanced signal (say (+2V) - (-2V) 4V) will go into a differential amplifier which will turn that into a single signal to go into the ADC.
The ADC will be able to cope with a full scale balanced signal of up to 4V
When you connect an unbalanced signal (say (+2V) - (0V) = 2V), you will only be using half the input range of the ADC. You could in fact (most likely, but depending on the supply voltage for the input stage) go up to 4V unbalanced and not saturate the input.
An alternative arrangement might be (though I very much doubt it would work like this) for the hot and cold signals from the input being separately fed into an ADC with a 2V range, and the summing done digitally afterwards. In this case it would not be possible to increase the unbalanced input beyond 2V.