Is it possible to mix the left and right inputs into a single ADC on the ADAU1961?
Yes, it can be done but you would have to ignore some of the "left" and "Right" labels to do it. You also cannot use the PGA.
So if you are using a microphone for an input source then you cannot mix the left and right signals into one ADC, you can only mix them on the output of the DACs.
If you have two single-ended audio sources then what you do is hook them up to the LINP and LINN inputs. You disable the PGA and enable the LINNG and LINPG. This will mix these two signals together with individual volume controls. Even though the signal pins are labeled "N" and "P" they do not invert the signals with respect to each other. These labels refer to the "N" and "P" inputs to the PGA. So you can sum three signals together using the LINN, LINP and LAUX signals. The summed signal is inverted. Then you can sum three different signals using the RINN, RINP and RAUX pins.
Let me know if you need more detail.