Hello.
No, they are not physically independent.
Here is a picture of the PCB to better understand ->
View attachment 436732
In '1' (green) these are the DAC chips ES9039Q2M, it has one per channel (right and left).
These DAC chips will deliver a CURRENT (I) output which will be converted into VOLTAGE (V) by the OPAMPS in '2' (orange) but also a low pass filtering.
In the case of the output signals on XLR sockets, these signals from the OPAMPS in '2' (orange) concerned by one of the channels (i.e. 2 OPAMPS per channel) will form what is called the 'hot spot' and the 'cold point' necessary for a balanced signal, the latter will first pass through a kind of 'digital relay' in '4' (yellow) before arriving at the socket concerned.
In the case of the output signals on the RCA jacks, the signals from the '2' (orange) OPAMPS that have formed what is called the 'hot spot' and the 'cold spot' for each channel will pass through the '3' OPAMP which will perform what is called a 'differential summation' in order to create a unique signal for each of the RCA channels (right and left).
Then this signal will in turn pass through a 'digital relay' in '4' (the middle one in yellow) to finally arrive at the RCA sockets.
So when you select on your DAC in the 'RCA + XLR' menu, all the 'digital relays' pass the signal and the outputs of the OPAMPS are somehow connected to each other, unless there are capacitors linking to their outputs but we don't have the circuit diagram....
... what is certain is that the more devices you connect to the different outputs of the DAC (RCA and XLR) the more you will expose yourself to possible 'ground loop' problems
That said: above each 'digital relay' we see
'MELF' resistors in series with the signal that serve to
protect the OPMPS upstream.
Moreover it seems that since each OPAMP output also provides a 'low-pass filter' function then a capacitor is in series with the signal, but without the diagram we are not sure of anything once again.