If you amplify almost any recording enough, you can get some form of noise. Any white noise of a sufficient duration is effectively a recording of that one John Cage piece.
no, it isn't, because that piece is unconscious- it is meant to be what happens without any intention. A crank up to noise is a definite intention of the performer. In 4'33", the performer does nothing but open the score and the keyboard, mark movements, and bow at the end.
If you go through enough generations of analog copies of a recording of that performance, you get 4'33" of noise.