Is the electronegativity value ever used in calculations, or is it just a number assigned to each element?
True, with values of electronegativity in hand (and beside the by Pauling, there are others by Rochow, Mulliken, etc. to name some scales) you describe bond polarity. Beyond this number, infrared vibrational frequencies, chemical shifts in NMR spectroscopy and isomer shifts in Mössbauer spectroscopy are mentioned by the corresponding wikipedia article.