Let's look at each of these in turn. First, as a number of posters have already pointed out, the USB audio protocol used by most DACs today is a synchronous protocol, very different from the packet-based protocols used to transmit data between a CPU and other types of peripherals. Synchronous digital transmission protocols, like SPDIF, AES, and synchronous USB, are transmitting both data and clock (timing) in the same analog-like waveform. Accurately recovering the data from that waveform is trivially simple compared with accurately recovering the timing. That is significant.
All digital audio systems exhibit some degree of timing error (aka jitter), which only becomes significant when the signal is transformed back to analog. Errors in timing of the data stream fed to the reconstruction filter(s) create distortion in the analog output. This distortion is enharmonic, and thus audible at much lower magnitudes than the harmonic distortion introduced by analog components and speakers. The magnitude of jitter-related distortion depends in a complex way on the characteristics of the jitter itself, as well as the encoded audio signal. None of this is controversial or unscientific; digital transmission jitter has been studied extensively, in both audio and other contexts.
Can cables impact jitter? Yes, in fact from the perspective of pure physics, it's impossible for a cable not to impact timing in a synchronous digital transmission system, because the signal itself is effectively like an analog waveform, containing very high frequency components. The interaction between the electrical characteristics of the cable, and the source and sink the cable is connected to, will change the shape of that waveform to some degree, and thus contribute to timing errors (jitter). How much those timing errors will impact the final analog signal depends in a very complex way on interactions between the cables, the transmitting and receiving circuits, the signal data itself, and the type and implementation of various clock recovery (de-jittering) schemes on the receiving end, but in general it is not possible to make a perfect de-jittering algorithm, and therefore not possible to make a synchronous digital transmission cable which will be perfectly "transparent" in the context of a complete system. So, in an absolute sense, the question of whether USB or SPDIF digital cables can impact the sound is pretty simple: of course they can. In fact, they almost must.