Studies on wireless network synchronization based on the theory of coupled oscillators largely ignore the interference caused by the in-band synchronization signals exchanged. We show that such interference can play a key role and find two basic insights: First, increasing the node transmission power does not necessarily lead to faster synchronization. Second, synchronization can be accelerated by randomly switching between two power levels while maintaining the overall average power consumption. This approach temporarily boosts the network connectivity with negligible impact on the average interference. As a special case, one of the power levels can be zero, linking this approach to the known concept of stochastic coupling. Results suggest that a randomization of the coupling – e.g., using fewer but stronger synchronization signals – can have benefits for self-organizing synchronization under consideration of~interference.