It’s kinda impossible to answer, since there are infinite possible ways to randomly generate noise, for instance

• White noise is en.wikipedia.org/wiki/White_noise
• Pink noise en.wikipedia.org/wiki/Pink_noise
• Brownian noise en.wikipedia.org/wiki/Brownian_noise Most random audio processes do not have a name. And if any audio is possible, like in these processes, you would never get an exact real song, but getting close (same as a real song but a little out of tune) would happen eventually.

I think a better analogy to infinite monkeys typing Shakespeare is randomly hitting the keys on a piano, though still, you would need to specify how the timing of the notes is randomized. If the lengths of the notes and the pauses are uniform and limited to standard lengths, eventually you would get, say Mozart’s Symphony no 5.