We investigate the interplay between quenching and strong coupling in systems that include a collection of quantum emitters interacting with a metal nanoparticle. By using detailed numerical simulations and analytical modeling, we demonstrate that quantum emitters can exhibit strong coupling with the particle dipole resonance at distances at which the quenching to nonradiative channels is expected to dominate the dynamics. These results can be accounted for in terms of the pseudomode character of the higher multipole modes of the nanoparticle and the corresponding reduction of the induced loss rate. These findings expand the current understanding of light-matter interaction in plasmonic systems and could contribute to the development of novel quantum plasmonic platforms.