Spectral population synthesis (PS) is a fundamental tool in extragalactic research that aims to decipher the assembly history of galaxies from their SED. However, until recently all PS codes were restricted to purely stellar fits, neglecting the essential contribution of nebular emission (NE). With the advent of FADO, the now possible self-consistent modelling of stellar and NE opens new routes to the exploration of galaxy SFHs. The main goal of this study is to quantitatively explore the accuracy to which FADO can recover physical and evolutionary properties of galaxies and compare its output with that from purely stellar PS codes. With this in mind, FADO and STARLIGHT were applied to synthetic SEDs that track the spectral evolution of stars and gas in extinction-free mock galaxies that form their stellar mass ($M_star$) according to different parametric SFHs. Spectral fits were computed for two different set-ups that approximate the spectral range of SDSS and CALIFA data. Our analysis indicates that FADO can recover the key physical and evolutionary properties of galaxies, such as $M_star$ and mass- and light-weighted mean age and metallicity, with an accuracy better than 0.2 dex. This is the case even in phases of strongly elevated sSFR and thus with considerable NE contamination. As for STARLIGHT, our analysis documents a moderately good agreement with theoretical values only for evolutionary phases for which NE drops to low levels. Indeed, fits with STARLIGHT during phases of high sSFR severely overestimate both $M_star$ and the mass-weighted stellar age, whereas strongly underestimate the light-weighted age and metallicity. The insights from this study suggest that the neglect of nebular continuum emission in STARLIGHT and similar purely stellar PS codes could systematically impact $M_star$ and SFH estimates for star-forming galaxies.
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