Interesting question, that must be tried. I guess it depends on negative in relation to what.
Hum is right that sound is opposite to zero in the time domain, but in frequency domain your proposed white noise could be seen as opposite to no sound. I will suggest pink noise due to the logarithmic behaviour of the human ear.
The SPL6 function Process/Imprint/Cast will do the job when imprinting the source signal to a noise signal.
So how does it sound? Well, a bit noisy For speech, most of the rhythmic information is maintained, but speech intelligibility is very bad. For pure singing some kind of pitch information is maintain, although the pitch seems to be shifted down four or five quartertones (at least in my example). Maybe loaded heavy rock will work better, I haven’t tried yet.
But it was a good opportunity to investigate the behaviour of FFT size, resolution, margin etc. especially when you combine the different results made with the same noise signal in reverse phase. But the last is more the Mold function than negative music.
Best regards Egebjerg