In LC VCOs, small-signal noise from various noise generators (bias current ,gm pair etc.) reach the tank and modulate the tank components mainly varactors diodes etc. The noise sources also change the amplitude of the oscillating signal and result in changing tank capacitance slightly. This mechanism changes frequency of oscillation as a function of small-signal noise resulting in AM-FM conversion.

My question is: Does pnoise capture this effect correctly?

Based on what I read about PSS and PNOISE, at each large signal operating condition, simulator generates a linear circuit and computes the transfer function of the noise at that bias point to the output. It does not talk about capacitor variation (or component variation) due to noise.