Aromatic compounds are well-known acceptors of primary radical ions that are formed under high-energy irradiation of nonpolar systems. Thus formed radical ion pairs recombine and produce magnetosensitive fluorescence, which helps study the short-lived radical ions. It was initially suggested that a simple introduction of a spin label into the original arene would allow an easy transition from two-spin to three-spin systems, retaining the experimental techniques available for radical pairs. However, it turned out that spin-labeled arenes often do not produce magnetosensitive fluorescence in the conditions of a conventional radiochemical experiment. To understand the effect of the introduced spin label, we synthesized a series of compounds with the general structure "stable 3-imidazoline radical-two-carbon bridge-naphthalene" as well as their diamagnetic analogues. By use of this set of acceptors, we determined the processes that ruin the observed signal and established their connection with the chemical structure of the compound. We found that the compounds with flexible (saturated) two-carbon bridges between the luminophore and the stable radical moieties exist in Solution in folded conformation, which leads to suppression of luminescence from naphthalene due to efficient through-space exchange quenching of the excited state by the radical. Increasing the rigidity of the bridge by introducing the double bond drastically increases the reactivity of the extended pi-system. In these compounds, the energy released upon recombination is spent in radiationless processes of chemical transformations both at the stage of the radical ion and at the stage of the electronically excited molecule.