Spectre does have transient noise.
For periodic circuits pnoise can still be used to predict accumulated jitter.
Have you see the analysis section of this website ?
try http://www.designers-guide.org/Analysis/PLLnoise+jitter.pdf

In Cadence Spectre, Transient Noise Analysis and Time Domain Noise Analysis exist.

Time Domain Noise Analysis is unique feature of SpectreRF(PSS/Pnoise).
http://www.designers-guide.org/Forum/YaBB.pl?num=1207830622/4#4

On the other hand, almost all simulator have transient noise analysis, e.g. ADS, Eldo, Spectre.

Do you intend a transient noise analysis or a time domain noise analysis ?

New Features in the MMSIM6.0 Release
Transient Noise
Transient noise provides the benefit of examining the effects of large signal noise on many
types of systems. It gives you the opportunity to examine the impact of noise in the time
domain on various circuit types without requiring access to the SpectreRF analyses. This
capability is an extension to the current transient analysis, and is accompanied by
enhancements to several calculator functions, allowing you to calculate multiple occurrences
of measurements such as risetime and overshoot. Spectre provides both a single run and
multiple run method of simulating transient noise. The single run method, which involves a
single transient run over several cycles of operation, is best suited for applications where
undesirable start-up behavior is present. The multiple run method, which involves a statistical
sweep of several iterations over a single period, is recommended for users who are able to
take advantage of distributed processing.
For more information, see Calculating Transient Noise in Chapter 6 of the Spectre Circuit
Simulator User Guide.