Context: The technique of matching synthetic spectra computed with theoretical stellar atmosphere models to the observations is widely used in deriving fundamental parameters of massive stars. When applied to binaries, however, these models generally neglect the interaction effects present in these systems Aims: The aim of this paper is to explore the uncertainties in binary stellar parameters that are derived from single-star models Methods: Synthetic spectra that include the tidal perturbations and irradiation effects are computed for the binary system alpha Virginis (Spica) using our recently-developed CoMBiSpeC model. The synthetic spectra are compared to S/N~2000 observations and optimum values of Teff and log(g) are derived. Results: The binary interactions have only a small effect on the strength of the photospheric absorption lines in Spica (<2% for the primary and <4% for the secondary). These differences are comparable to the uncertainties inherent to the process of matching synthetic spectra to the observations and thus the derived values of Teff and log(g) are unaffected by the binary perturbations. On the other hand, the interactions do produce significant phase-dependent line profile variations in the primary star, leading to systematic distortions in the shape of its radial velocity curve. Migrating sub-features (bumps) are predicted by our model to be present in the same photospheric lines as observed, and their appearance does not require any a priori assumptions regarding non-radial pulsation modes. Matching the strength of lines in which the most prominent bumps occur requires synthetic spectra computed with larger microturbulence than that required by other lines.