The quality of a digital interconnects makes no difference. The sender merely sends a stream of bytes at a clock rate. If this becomes distorted due to interferrence then either i) the bits won't get there and you get pixellation/stutter ii) the bits get jumbled up and you still get pixelation/stutter. Pictures and sound are not decoded in such a way that a slight change in a bit stream would change colour or sound quality, instead a slight change would completely change the picture or sound (most often resulting in no picture or sound for a slight moment).
Think about your DAB or freeview box because the principle is the same. If you have a bad signal (the transmission is simple sending a stream of bytes to make up an mpeg decoding to your aerial, so there loads of interferrence there) your tv picture stutters, otherwise you get a picture. The picture, put simply, is either there or it isn't. There's no inbetweeen. For a HDMI cable, you really won't see problems until you start using cables greater than 15m, which is a limit in the technology, not the cable.