Most of the tests proposed in the literature to verify if a given random multivariate dataset fits a spherical or elliptical distribution are designed for real valued data and rely on the estimation of high order moment matrices. Recently, a test that considers complex random vectors, derived based on the Schott spherical symmetry test was proposed aiming in a more proper analysis of PolSAR data. Results showed its effectiveness in discriminating data that fits or not the complex spherically invariant random vector model (product model), inherent to high resolution heterogeneous PolSAR systems. Within this context, this paper further extends the assessment of the referred test efficiency, verifying its performance under different stochastic model assumptions and comparing the results with the ones achieved when the Schott test derived for real random vectors is employed.