Most neutron stars? I would think not. The cooling time for a neutron star is initially seconds due to neutrino emission and thermal conduction is very effective, so the bulk of the neutron star will be isothermal. There will be a thin non-degenerate layer on top of the crust with a big temperature drop to the "photosphere". By the time a neutron star is a few years old, its surface will be $<10^7$ K and maybe $10^6$ K after 1000 years. These temperatures are far too low to produce significant thermal radiation above 10 keV. Of course, the interior could be a factor of $\sim 100$ hotter and will produce hard X-rays, but these will not escape because the layers above will be thick to Compton scattering and inverse bremsstrahlung, which involve both nuclei and electrons.
There will however be a soft X-ray photosphere in young neutron stars. Opacity will be provided by the photoelectric effect, Compton/Thomson scattering and inverse bremsstrahlung.
The "photosphere" becomes just about detectable at (soft) X-ray energies during accretion bursts from companion stars (e.g. Cottam et al. 2008). But even here, the thermal spectrum is only a few keV in temperature. This is still far too cool to produce gamma rays, but there are observations that show (perhaps) absorption features in the soft X-ray spectrum in much the same way as we see Fraunhofer lines in the visible solar photosphere. The burst spectrum is contaminated though by elements in the accreted material.
The X-ray photospheric spectrum during an X-ray burst (from Cottam et al. 2008).
Hard X-rays and gamma rays from neutron stars will not be photospheric, they will arise from non-thermal processes associated with charged particle acceleration in the strong electromagnetic fields that likely thread the surface.