Modular architectures are a promising approach to scaling quantum computers beyond the limits of monolithic designs. However, non-local communications between different quantum processors might significantly impact overall system performance. In this work, we investigate the role of the network infrastructure in modular quantum computing architectures, focusing on coherence loss due to communication constraints. We analyze the impact of classical network latency on quantum teleportation and identify conditions under which it becomes a bottleneck. Additionally, we study different network topologies and assess how communication resources affect the number and parallelization of inter-core communications. Finally, we conduct a full-stack evaluation of the architecture under varying communication parameters, demonstrating how these factors influence the overall system performance. The results show that classical communication does not become a bottleneck for systems exceeding one million qubits, given current technology assumptions, even with modest clock frequencies and parallel wired interconnects. Additionally, increasing quantum communication resources generally shortens execution time, although it may introduce additional communication overhead. The optimal number of quantum links between QCores depends on both the algorithm being executed and the chosen inter-core topology. Our findings offer valuable guidance for designing modular architectures, enabling scalable quantum computing.