Yes the external clock adds jitter which the simplest of jitter (random jitter) will increase your noise floor. More complex jitter makes for all sorts of undesired at frequencies that depend on the music, but at frequencies that are not musical harmonics.However you talk exclusively about adding environmental (uncorrelated) noise to the sound you hear. It cause harmonic distortions, responsive for colouration.
We are talking about 2 separate things.
I’m talking about an external clock causing increases of jitter, and harmonics.
I am not talking about an internal clock, nor am I talking about dither.
I listed a bunch of jitter causing reasons why this is not so.. It is why moving the clock outside is beneficial.
It is exposed to a noise which is dependant on the sound currently played. Jitter shape is modified accordingly to the sound. Then a modified such way clock signal is used for D/A conversion.
If you are implying here that you can add jitter on purpose to alter a tone to have it sound better, OK sure. You can alter a fixed tone with jitter, and can argue that you like it, but the alteration has to be deliberate for a specific constant tone (including fixed amplitude). You change the tone and the distortion changes... Jitter distortions are an INTERACTION between the clock timing AND THE MUSIC. The last I heard, music is not a constant fixed tone.
Again though we are not talking about the same thing that I have been talking about.