Superhydrogenated polycyclic aromatic hydrocarbons (PAHs) have been suggested to catalyze the formation of H-2 in certain regions of space, but it remains unclear under which circumstances this mechanism is viable given the reduced carbon backbone stability of superhydrogenated PAHs. We report a laboratory study on the stability of the smallest pericondensed PAH, pyrene (C16H10+N, with N = 4, 6, and 16 additional H atoms), against photodestruction by single vacuum ultraviolet photons using the photoelectron-photoion coincidence technique. For N = 4, we observe a protective effect of hydrogenation against the loss of native hydrogens, in the form of an increase in the appearance energies of the C16H9+ and C16H8+ daughter ions compared to those reported for pristine pyrene (C16H10). No such effect is seen for N = 6 or 16, where the weakening effect of replacing aromatic bonds with aliphatic ones outweighs the buffering effect of the additional hydrogen atoms. The onset of fragmentation occurs at similar internal energies for N = 4 and 6, but is significantly lower for N = 16. In all three cases, H-loss and CmHn-loss (m >= 1, carbon backbone fragmentation) channels open at approximately the same energy. The branching fractions of the primary channels favor H-loss for N = 4, CmHn-loss for N = 16, and are roughly equal for the intermediate N = 6. We conclude that superhydrogenated pyrene is probably too small to support catalytic H-2-formation, while trends in the current and previously reported data suggest that larger PAHs may serve as catalysts up to a certain level of hydrogenation.