The per-element hardness and electronegativity are just parameters fitted to the electron affinities and ionization energies. The equilibrium charges on atoms are determined from the instantaneous environment to equalize the charge force (energy wrt charge). So yes, to some extent the QEq parameters can describe both the neutral and ionized states. But there are quite a few papers discussing the drawback of the QEq approach and there have been several new charge equilibration methods. Please see the literature for these papers.
You can develop and implement a new charge equilibration method for ReaxFF, but of course you would have to modify the LAMMPS source code.