Can white Gaussian noise improve signal level in non-linear device? In the system shown below, can white Gaussian noise amplify or attenuate the input signal?


Most of the time we check signal level proportional to noise level (such as noise figure) not singly.

I have obtained PSD of my desire system's output and it is a combination of 


a) Dc term
b) reaction of input noise to itself 
c) reaction of input signal to itself 
d) reaction of input signal and input noise.


At system's output at frequency $\omega$ should I assume terms (c) and (d) as the signal level? Or c is enough?
As Jason R. says in the comment, dither will do this.  Another phrase to look for is noise shaping where the noise spectrum can be reshaped to not interfere with the signal of interest.