Again: If it's only about noise (and that antenna effect is exactly that), you can just capture that with an ADC like an ADI 2 FS Pro. I don't understand what any shielding of that ADC would do to the input signal noise. The ADC captures what the DAC outputs, so it effectively replaces the amp in the playback chain. If the DAC is "affected" by that noise, it will be present at the DAC outputs and will be captured by the ADC.
Differences in the grounding scheme of the whole setup including the ADC will affect ground loops and noise, but that problem will also affect any real system with an amp.
If it is only about noise, you could also simply play a silent track and then listen for or record the noise using a microphone, if you insist on an air gap. There is no need for playing music and complex double blind testing if you just want to determine if any EMI induced noise is present in the DAC output.
@Salida is correct that the USB audio protocol lacks error correction. However, in my experience, bit errors in audio transmission are
not subtle. If you ever listened to a portable CD player with an undersized playback buffer or tinkered with individual samples in Audacity, you will remember how jarring such tiny errors can sound