Yes, a good HDMI cable does make different in term of quality. In high speed digital transmission, it's not simple as '0' and '1' only especially dealing with gigabit transfer rate. There is a lot factor to consider and the basic is the propagation delay, such as setup time and hold time, they are in nanosecond scale. As the result, the receiver might interpret the wrong info.

I can explain more if you guys want to understand more, but it is going to be very technical.