Under generic and physiologically relevant conditions we show that self-organization to the edge of synchronization transition is achieved in networks of Izhikevich spiking neurons as a joint result of spike-timing dependent plasticity (STDP) and time delay associated with axonal conduction (Khoshkhou and Montakhab, Front. Sys. Neurosci. 2019). STDP is also believed to be a cornerstone concept in learning. Since the phenomenon of learning and self-organization to the edge of synchronization transition can emerge jointly in spiking neural networks as a result of STDP, it is tempting to ask whether learning performance benefits from synchronization and/or such self-organization? To address this question we employ a reinforcement learning rule implemented through dopamine-modulated STDP to indow the above network with the ability of learning stimulus-response tasks. We find that the system similarly exhibits a continuous transition from synchronous to asynchronous neural oscillations upon increasing the average axonal time delay. We characterize the learning performance of the system and observe that it is optimized near the synchronization transition point. Inspection of neuronal avalanches in the system provides evidence that optimized learning performance is achieved in a slightly synchronized (supercritical) state (Khoshkhou and Montakhab, Phys. Rev. E 2022).