Have a look at this table, which shows the binding energy (i.e. the ionisation energy) of electrons in various atoms. The highest energies are a few hundred eV, and those are for the core electrons (though admittedly it doesn't show $1s$ energies for the heavy atoms) so the average electron binding energy will be lower.
By contrast, the average binding energies of nucleons is around 8 MeV. So in general the binding energy of the nucleons will be much greater than the binding energy of the electrons, and the mass deficit will be dominated by the nucleus.
But I'm not sure it makes much sense to just add together electron and nucleon binding energies to get a total binding energy for the atom. I suppose it does have a meaning in that it is the energy necessary to dismantle the atom into separate electrons, protons and neutrons. In practice it's hard to see how this ever be useful.
It is possible to work out the mass deficit due to the electron binding energy in the hydrogen atom. Obviously in this case the nucleus is just a proton so there is no nuclear binding energy. The masses of the proton, electron and hydrogen atom are precisely enough known to (just) be able to calculate the mass deficit. The mass deficit is of course 13.6eV.