Could you confirm if the LAUX And RAUX inputs can be simultaneously ADC processed as well as played through LHP and RHP ?
If not, how much would be lag in between the input and output?
They are simultaneously sampled and the DACs are also independent so no need to multiplex so there will be no lag between the two DACs.
Now rereading your question I think you are asking about input and output delay, so the group delay?
In this part there is an analog path that can go from the input mixers directly to the output mixers and to the line output drivers. Avoiding any ADC or DAC conversions. So the group delay will be very small. It is never zero since there is a delay just going though an OpAmp but it will be very small. I am not certain what it is but it can easily be measured.
The ADC can be converting this signal and sending it out of the serial port at the same time. If you download SigmaStudio and look at the hardware config and the register settings there is a good block diagram of the record and playback signal paths which will answer these questions.