The detection of the carrier-envelope offset frequency (fCEO) of optical signal

[Lithium_Niobate_Dog]

TL;DR Summary

When detecting fCEO using an f-2f interferometer, does the phase noise transmitted to the detected fCEO become relatively larger as the value of frep increases?

Assuming the noise sources are exactly the same, the phase noise of the repetition rate (frep) of an optical frequency comb (OFC) increases as the absolute value of frep increases. In this case, can we assume that the phase noise of the fCEO detected using an f-2f interferometer also increases relatively as the absolute value of the OFC's frep increases?
In other words, is it correct to say that as frep increases, the amount of noise transmitted to fCEO also increases?