Comparing energies of isoelectronic species, but one protonated
I think they can and should be compared. Consider the $\ce{H_2^+}$ molecular ion. When dissociating this correctly (that is, including symmetry breaking), one should eventually end up with $\ce{H}+\ce{H^+}$. One can then extract the dissociation energy of the bond from the calculations. This is equivalent to the proton affinity of atomic $\ce{H}$. By applying this logic to larger species, one reaches the conclusion, that yes, $\ce{H+}$ by definition has zero energy and should enter calculations of relative energies as such.

As an aside, the calculation of negatively charged species in the gas-phase can lead to erroneous results, but any argument made for $\ce{A-/AH}$ will certainly hold for $\ce{B/BH^+}$.