They mention "large signal noise" in the context of Transient Noise Analysis and mean nonlinear effects of noise. Traditional Noise Analysis linearizes the circuit around the DC operating point (just like AC Analysis) and does not show nonlinear effects of noise.

Pnoise Analysis linearizes the circuit around the periodic operating point and does not show nonlinear effects of the noise either. However, it does show nonlinear effects of the periodic signals in the circuit (like mixing), also with respect to the noise.