No, a "double-wide" AES/EBU connection does not segregate clock from data. Although I'm not particular familiar with the dCS equipment, and it's conceivable to me that some of its many possible configurations may involve a proprietary variant of AES/EBU that does do that. But aside from that possibility, which strictly speaking would not be AES/EBU compliant, all that is segregated is the left channel from the right channel. And that is certainly the case with the Musical Fidelity unit. I2S, on the other hand, does segregate clock from data.
None of these approaches "skip the whole clocking process." What is skipped in I2S is the need for the DAC to extract the clock from the single signal that contains both clock and data in the case of an AES/EBU or S/PDIF connection. That extraction process can contribute to jitter.
"Coax" (short for coaxial cable) is a type of cable; "BNC" is a type of connector. Coax cable can be used with BNC, RCA, or other types of connectors, and carries an unbalanced signal. AES/EBU is usually used with XLR connectors, in the form of a balanced signal pair, but may also be transmitted as an unbalanced signal via BNC connectors and coaxial cable (mainly in some professional applications).
As far as the original question is concerned, the "double-wide" configuration allows the design to essentially be dual mono, and allows a given data rate to be communicated between transport and DAC at a clock frequency that is lower by a factor of 2. Perhaps there are some other potential advantages, as well. As usual, though, I'd expect that the quality of a particular implementation will be more important than the design approach that is used.