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Ok, some technote from my side, sorry… 😉
For proper digital connections between audio gear a global clock reference needs to be established. I’m not talking about everything switched to the same sampling rate (which is a prerequisite) but for sample clock on all units running in sync.
Even with everything set to 48kHz, for example, any oscillator still has some tolerance (~100ppm). So one unit may run with 48.000,1 Hz, the next one with 47.999,8Hz.
Word Clock in/out is the magical word here. Even if word clock could be extracted from ADAT or S/PDIF streams, it is far more reliable and provides less clock jitter (turns into noise when converted to analog) to run a separate BNC cable for the word clock.
There is exactly one Word Clock Master providing the reference and one or more slaves synchronizing their (internal) clock generators to that word clock (using PLL/DLL/VCXO or similar technology).

With everything running in the same word clock domain no resampling is required at all. If the units are not synced, resampling is required (on a sub-sample basis) or you’ll hear a click from time to time.

Bob’s scenario may work, if the ADAT card is able to synchronize to the clock reference from the Qu (via USB), but this would require some generic API within the OS which is aware of clock domains at all. Nothing a PC will do, maybe CoreAudio on Mac, not sure. ASIO is not an option, since you only can use one ASIO driver per application, for the same reason (not synchronizable).

I’d probably prefer an analog connection… 😉