[Abridged] In recent works we have proposed two new large-angle non-Gaussianity indicators based on skewness and kurtosis of patches of CMB sky-sphere, and used them to find out significant deviation from Gaussianity in frequency bands and foreground-reduced CMB maps. Simulated CMB maps with assigned type and amplitude of primordial non-Gaussianity are important tools to determine the strength, sensitivity and limitations of non-Gaussian estimators. Here we investigate whether and to what extent our non-Gaussian indicators have sensitivity to detect non-Gaussianity of local type, particularly with amplitude within the seven-year WMAP bounds. We make a systematic study by employing our statistical tools to generate maps of skewness and kurtosis from several thousands of simulated maps equipped with non-Gaussianity of local type of various amplitudes. We show that our indicators can be used to detect large-angle local-type non-Gaussianity only for relatively large values of the non-linear parameter $f_{rm NL}^{rm local}$. Thus, our indicators have not enough sensitivity to detect deviation from Gaussianity with the non-linear parameter within the seven-year WMAP bounds. This result along with the outcomes of frequency bands and foreground-reduced analyses suggest that non-Gaussianity captured in the previous works by our indicators is not of primordial origin, although it might have a primordial component. We have also made a comparative study of non-Gaussianity of simulated maps and of the full-sky WMAP foreground-reduced seven-year ILC-7yr map. An outcome of this analysis is that the level of non-Gaussianity of ILC-7yr map is higher than that of the simulated maps for $f_{rm NL}^{rm local}$ within WMAP bounds. This provides quantitative indications on the suitability of the ILC-7yr map as a Gaussian reconstruction of the full-sky CMB.
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