Do all the electrons that absorb a photon come out as photoelectrons?

NO, all electrons absorbing photons may not come out as photoelectrons. Any electron can come out as a photoelectron if and only if it gains enough energy to overcome the attractive force of the nucleus. The electrons farther away from the nucleus experience a smaller attractive force than those near the nucleus. Thus, they both require different energies to be able to come out as photoelectrons. An electron is able to come out of the metal if and only if it’s energy becomes greater than the work function of the metal.