Transient simulations usually cannot include the noise of devices.
(Not in Spectre, not in HSPICE)
I heard Eldo is able to run transient simulations with the noise parameters of devices included.
According to the attached PDF paper, Eldo has this capability as early as year 2002.
To save your 信元, the name of this paper is "A New and Efficient Transient Noise Analysis Technique for CCD Image Sensors or Particle Detectors."