The energetic lowest state of a composite particle is the ground state of a many particle system. That is the case if the inertial mass mi(NP,NE,Ne,Np) is zero. Thus, if
(NP+NE)∙mP +(Np+Ne)∙me = E((NP,NE,Ne,Np),bound)/c^2.
The ground state of the hydrogen atom at the bound energy E(H,bound) = 13.8 eV is surely not the ground state of the proton-electron two-particle system.