I think the quality of the cable plays a role, though, even in balanced mode.
What plays a much larger role in the sound of the cable is how its constructed (as opposed to quality), which is to say that if done correctly it will be a twisted pair within a shield.
Beyond that, the shield is ignored both at the input and output of the cable. If this is not the case, then the construction of the cable will become audible. This is why the balanced standard specifies that the shield connection is for shielding only and not signal return.
This fact if often ignored in both high end audio and also in some studio gear! It is also why there are high end uber expensive balanced cables now.