Due to their heavily obscured central engines, the growth rate of Compton-thick (CT) active galactic nuclei (AGN) is difficult to measure. A statistically significant correlation between the Eddington ratio, {lambda}$_{Edd}$, and the X-ray power-law index, {Gamma}, observed in unobscured AGN offers an estimate of their growth rate from X-ray spectroscopy (albeit with large scatter). However, since X-rays undergo reprocessing by Compton scattering and photoelectric absorption when the line-of-sight to the central engine is heavily obscured, the recovery of the intrinsic {Gamma} is challenging. Here we study a sample of local, predominantly Compton-thick megamaser AGN, where the black hole mass, and thus Eddington luminosity, are well known. We compile results on X-ray spectral fitting of these sources with sensitive high-energy (E> 10 keV) NuSTAR data, where X-ray torus models which take into account the reprocessing effects have been used to recover the intrinsic {Gamma} values and X-ray luminosities, L$_X$. With a simple bolometric correction to L$_X$ to calculate {lambda}$_{Edd}$, we find a statistically significant correlation between {Gamma} and {lambda}$_{Edd}$ (p = 0.007). A linear fit to the data yields {Gamma} = (0.41$pm$0.18)log$_{10}${lambda}$_{Edd}$+(2.38$pm$ 0.20), which is statistically consistent with results for unobscured AGN. This result implies that torus modeling successfully recovers the intrinsic AGN parameters. Since the megamasers have low-mass black holes (M$_{BH}approx10^6-10^7$ M$_{sol}$) and are highly inclined, our results extend the {Gamma}-{lambda}$_{Edd}$ relationship to lower masses and argue against strong orientation effects in the corona, in support of AGN unification. Finally this result supports the use of {Gamma} as a growth-rate indicator for accreting black holes, even for Compton-thick AGN.
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