What is the spectrum of modulated noise?
Short answer: most likely white noise.

Long answer:

Amplitude modulation using a sinusoidal wave shifts the original spectrum in frequency by the sinusoids frequency.  For instance, if there is a source with a square spectrum spanning -100Hz to 100Hz, and it is modulated by a 1000Hz sinusoid, it will have shifted the spectrum in both positive and negative frequency.  Thew new spectrums will show two sources of energy from -1100Hz to -900Hz and 900Hz to 1100Hz.


To answer your question, we also should consider that their source signal is white-noise, and the carrier signal is a square wave rather than a sinusoid.  A square wave, rather than having a single peak in the frequency domain (such as a sinusoid does), has multiple harmonics of descending strength.  Modulating with a square wave will create multiple images of your source signal to appear, each centered around the square wave's harmonics and scaled by the half the strength of the harmonic. 


If your input signal is true white noise (really only observed mathematically), the shifted noise signals would only add up to more white noise.  But, if you have band-limited noise, then you will see copies of the noise spectrum shifted to the square wave's harmonics.