USB stands for universal serial bus, so all processes run in series.
A clarification: "Serial" in the context of a data bus such as USB doesn't refer to processes. It refers to the fact that the bits are transmitted through the USB interface one after another, on the same wire. Or more precisely, on each of two wires, since USB utilizes a balanced pair of signals, which are the same except that the polarity of one is inverted relative to the other.
The opposite of a serial bus would be a parallel bus, in which (to cite a hypothetical example) the 16 or 24 bits of audio data (per sample per channel) would be transmitted simultaneously on 16 or 24 parallel wires (or balanced pairs of wires). That is not done for reasons of practicality, cost, etc., given that serial bus technology is available with sufficient speed to communicate the bits one after another.
That said, it is certainly conceivable that the amount of noise and jitter on the USB interface to a DAC could be affected to some degree by the type of drive and drive interface that is being used.
Best regards,
-- Al