Does using fake cables damage the adapter?

Using a "fake" charging cable could be problematic if that cable cannot support the current passing through it, or has too high of a resistance. If either is the case, then it may be possible that this cable can overheat and catch on fire ... which could not only damage the cable, but anything it is attached to on either end.

What "adapter" are you referring to? An Apple power adapter? Something else? Connect it to what device?

suppose in theory, if their connector sizes somehow physically damages the connector it connects to