We have, of course, borrowed this word from visual terminology. A perfectly transparent piece of glass would be perfectly invisible; it would not alter the image passing through it in any way. So if we are, at least, going to be true to what we've borrowed, the output of the perfectly transparent audio component would be exactly the same as the input, with the exception of amplitude. Purely theoretical, of course, this perfection does not exist, but nonetheless, Ethan is right...
With a transparent audio device in the audio path, you won't hear a difference when switching between Engaged and Bypassed
...except, of course, if the component in question is the amplifier, in which case you won't hear anything at all when it is bypassed. Unless there was
another amp in the signal chain...but of course distortions in the second amp (or the transducers) could mask the distortions of the first amp, making it
sound transparent, even if it were not.
Audio is hard, huh?
Of course we could
measure. Six ways to Sunday. Not allowing the component in question to be soiled by anything, just see if the signal coming out of it is the same as the one going in. But we don't have measurements for the known unknowns, or the unknown unknowns, and they could be anything we hear or don't hear. Anything. So we can borrow a term that has a clear (pun intended) meaning, and we can use it to mean almost anything at all.
Tim