Suppressing self-excited thermoacoustic oscillations in combustion chambers is essential for gas turbine system stability. Passive acoustic damping devices such as Helmholtz resonators are commonly employed in modern combustors to address the problem of thermoacoustic instabilities. The estimation of deterministic parameters characterizing flame-acoustic coupling, specifically the stability margins and linear growth/decay rates, is a prerequisite for designing these devices. As gas turbine combustors are typically noisy systems due to the presence of highly turbulent flows and unsteady combustion, it is essential to understand the role of noise and its impact on the estimated system stability. Recently several new results on the stochastic dynamics of thermoacoustic systems and the use of noise-induced dynamics to estimate system stability characteristics have been reported. In the present work, we study the different approaches previously reported on the estimation of linear growth/decay rates from noise-induced dynamics on an electroacoustic Rijke tube (a prototypical thermoacoustic system) simulator. We estimate the growth rates from noisy data obtained from the subthreshold, bistable, and linearly-unstable regions of the observed subcritical Hopf bifurcation and investigate the effect of additive noise intensity. We find that the noise intensity affects the stability boundaries and the estimated growth rates.