This research analyzes the mutual self-organized synchronization of phase-locked loops (PLLs) in the presence of variations in the free-running frequency of a PLL. In contrast to traditional synchronization methods that rely on a reference signal, this study investigates the synchronization dynamics that arise solely from the interactions of PLL nodes within a network. Previous research has proposed theoretical frameworks that can predict the synchronized states of such designs. However, these frameworks do not account for the dynamic behavior that occurs during initial synchronization. To address this gap, this work proposes a constraint that refines the understanding of initial synchronization. The results of this analysis show that there is a maximum detuning between free-running frequencies up to which synchronization is possible. Furthermore, this analysis indicates that detuning not only affects the range of time delays at which stable synchronized states emerge between PLL nodes, but also limits the allowable range of initial phase differences for stable synchronization. In the cases studied, a frequency difference of 1.56% reduces the probability of achieving stable synchronized states through self-organized synchronization to 73.5%, while no stable synchronization can be achieved at a frequency difference greater than 2.65%. The study underscores the critical importance of operating ranges when implementing mutual coupling. In particular, all PLL nodes must have overlapping lock ranges to achieve stable synchronization. It also emphasizes the need for accurate analysis of hold and lock ranges in relation to the time delays between coupled PLL nodes.